on some results in fuzzy metric spaces abstract we define a hausdorff topology on a fuzzy metric space introduced by kramosil and michalek kybernetica 11 1975 326 334 and prove some known results of metric spaces including baire s theorem for fuzzy metric spaces

on probabilistic φ contractions on menger spaces abstract recently ciric lj b ciric solving the banach fixed point principle for nonlinear contractions in probabilistic metric spaces nonlinear anal 72 2010 2009 2018 obtained a fixed point theorem with the intention to get a probabilistic version of the boyd wong theorem d w boyd j s w wong on nonlinear contractions proc amer math soc 20 1969 458 464 we give a counterexample to the key lemma of ciric and we establish a corrected version of his main theorem we also discuss the relations between our result and fixed point theorems of browder f e browder on the convergence of successive approximations for nonlinear functional equations nederl akad wetensch proc ser a 71 indag math 30 1968 27 35 and matkowski j matkowski integrable solutions of functional equations dissertationes math rozprawy mat 127 1975 68 pp

on some results of analysis for fuzzy metric spaces abstract a necessary and sufficient condition for a fuzzy metric space to be complete is given we prove that a subspace of a separable fuzzy metric space is separable and every separable fuzzy metric space is second countable uniform limit theorem is generalized to fuzzy metric spaces

on the knuth bendix completion for concurrent processes abstract we consider critical pairs for replacement systems over free partially commutative monoids this is done in order to apply the knuth bendix completion procedure to concurrent processes we will see that there are one rule systems which have no finite set of critical pairs therefore we develop a sufficient and computable condition such that finite trace replacement systems have a finite set of critical pairs this condition is always satisfied in the purely free case of semi thue systems or purely commutative case of vector replacement systems in fact it generalizes and unifies both cases we will give examples of how one can use this generalization

fixed points for fuzzy mappings in this paper the problem of the existence and computation of fixed points for fuzzy mappings is approached a fuzzy mapping r over a set x is defined to be a function attaching to each x in x a fuzzy subset r of x an element x of x is called fixed point of r iff its membership degree to r is at least equal to the membership degree to r of any y x i e r r y y x two existence theorems for fixed points of a fuzzy mapping are proved and an algorithm for computing approximations of such a fixed point is described the convergence theorem of our algorithm is proved under the restrictive assumption that for any x in x the membership function of r has a complementary function examples of fuzzy mappings having this property are given but the problem of proving general criteria for a function to have a complementary remain open

a note on fixed point theorems of hadzci c abstract in this paper we give a fixed point theorem for multi valued probabilistic contraction mappings on a menger space as a special case a fixed point theorem for multi valued contraction mappings on a fuzzy metric space is obtained the results presented improve and generalize in a sense some recent fixed point theorems proved by had ic

common fixed point theorems in fuzzy metric spaces in this paper we prove common fixed point theorems for six mappings in fuzzy metric space our main results extend generalize and fuzzify some known results in fuzzy metric spaces probabilistic metric spaces and uniform spaces

the complexity probabilistic quasi metric space we introduce and study a probabilistic quasi metric on the set of complexity functions which provides an efficient framework to measure the distance from a complexity function f to another one g in the case that f is asymptotically more efficient than g in this context we also obtain a version of the banach fixed point theorem which allows us to show that the functionals associated both to divide and conquer algorithms and quicksort algorithms have a unique fixed point

a fixed point theorem for contractive type fuzzy mappings abstract in this paper we define a contractive type fuzzy mapping and show that a contractive type fuzzy mapping has a fixed point on a complete metric linear space

coincidence theorems and variational inequalities for fuzzy mappings abstract in this paper some coincidence theorems and existence theorems of solutions of variational inequalities for fuzzy mappings are established

fixed degree for fuzzy mappings and a generalization of ky fan s theorem abstract in this paper the concept of some properties of fixed degree for fuzzy mappings are introduced and studied the results presented generalize and unify some recent results

coincidence degree and coincidence theorems for fuzzy mappings abstract in this paper the concept of coincidence degree and some coincidence theorems for fuzzy mappings have been introduced and established the results presented in this paper generalize and unify some results of 2 3 4 5 8 and give a fuzzy generalization of the famous kakutani ky fan theorem

coupled fixed point theorems for contractions in fuzzy metric spaces in the present work we prove a coupled fixed point theorem for contractive mappings in complete fuzzy metric spaces

fuzzy mappings and fixed point theorems abstract we extend heilpern s fixed point theorem for fuzzy contraction mappings to a pair of generalized fuzzy contraction mappings also we prove a fixed point theorem for nonexpansive fuzzy mappings on a compact star shaped subset of a banach space

an alternative characterization of probabilistic menger spaces with h type triangular norms abstract the class of h type triangular norms was introduced for the first time by had ic in 1978 in this paper a new characteristic property of the h type triangular norm is presented by virtue of this alternative characterization the continuity of quasi metrics and quasi norms is studied and some properties of the probabilistic menger spaces with this triangular norm are considered as applications new fixed point and fixed degree theorems for probabilistic nonlinear contractions and fuzzy mappings are given

fixed point theorems for fuzzy mappings in complete metric spaces in this paper we are concerned with mathematical properties of the previous contractive types of set valued maps or fuzzy mappings on a metric space see for instance nadler pacific j math 30 1969 475 488 heilpern j math anal appl 83 1981 566 569 papageorgiou nonlinear anal theory methods appl 7 1983 763 770 bose and sahani fuzzy sets and systems 21 1987 53 58 som and mukherjee fuzzy sets and systems 33 1989 213 219 park and jeong fuzzy sets and systems 59 1993 231 235 87 1997 111 116 lee et al fuzzy sets and systems 101 1999 143 152 and we prove some crucial theorems relating fixed points of fuzzy mappings on complete metric spaces first we prove a theorem by using the concept of w distance kada et al math japonica 44 1996 381 391 which generalizes the results of amemiya and takahashi fuzzy sets and systems 114 2000 469 476 and kada et al 1996 next we prove two theorems for fuzzy mappings which are connected with fixed point theorems for set valued maps then we shall observe that our theorems can be used to obtain almost all results proved so far concerning fixed points of fuzzy mappings or set valued maps on complete metric spaces and therefore that our results imply the existence of fixed points of various contractive types of fuzzy mappings or set valued maps on complete metric spaces

recognizable subsets of some partially abelian monoids we show that in a free partially abelian monoid generated by a finite alphabet a the subset x of a containing all the words equivalent to a product of words of x is rational if x is a finite set of words each word containing at least one occurrence of any letter of a we suppose that the graph the vertices of which are letters of a and the edges of which correspond to noncommuting pairs of letters is connected

quicksort algorithm application of a fixed point theorem in intuitionistic fuzzy quasi metric spaces at a domain of words in this paper we apply an intuitionistic fuzzy quasi metric version of a fixed point theorem to obtain the existence of solution for a recurrence equation associated with the analysis of quicksort algorithms

fixed points in fuzzy metric spaces abstract in this note the well known fixed point theorems of banach and edelstein are extended to fuzzy metric spaces in the settle of kramosil and michalek

triangular norms position paper i basic analytical and algebraic properties we present the basic analytical and algebraic properties of triangular norms we discuss continuity as well as the important classes of archimedean strict and nilpotent t norms triangular conorms and de morgan triples are also mentioned finally a brief historical survey on triangular norms is given

a comparative study of fuzzy norms on a linear space in this paper a comparative study among several types of fuzzy norms on a linear space defined by various authors has been made and it is shown that broadly they may be classified into two types one of which is katsaras s type and the other is felbin s type

nonlinear contraction theorems in probabilistic spaces abstract in this paper first we prove a common fixed point theorem in menger probabilistic metric spaces then we present a nonlinear contraction case of jungck s common fixed point theorem in menger probabilistic metric spaces finally we prove a common fixed point theorem for six self maps in a menger probabilistic metric space

fixed degree and fixed point theorems for fuzzy mappings in probabilistic metric spaces abstract this paper introduces the concept and properties of fixed degrees for fuzzy mappings in probabilistic metric spaces by virtue of this concept some theorems about common fixed degree of a sequence of fuzzy mappings in probabilistic metric spaces are obtained these new results are a unified approach to generalize several fixed point theorems for fuzzy mappings

altering distances in probabilistic menger spaces abstract altering distance functions in probabilistic fixed point theory have been recently considered by b s choudhury and k das in this paper we establish some fixed point results involving altering distances in complete probabilistic menger spaces under t norms weaker than the t norm min

person re identification by dual regularized kiss metric learning person re identification aims to match the images of pedestrians across different camera views from different locations this is a challenging intelligent video surveillance problem that remains an active area of research due to the need for performance improvement person re identification involves two main steps feature representation and metric learning although the keep it simple and straightforward kiss metric learning method for discriminative distance metric learning has been shown to be effective for the person re identification the estimation of the inverse of a covariance matrix is unstable and indeed may not exist when the training set is small resulting in poor performance here we present dual regularized kiss dr kiss metric learning by regularizing the two covariance matrices dr kiss improves on kiss by reducing overestimation of large eigenvalues of the two estimated covariance matrices and in doing so guarantees that the covariance matrix is irreversible furthermore we provide theoretical analyses for supporting the motivations specifically we first prove why the regularization is necessary then we prove that the proposed method is robust for generalization we conduct extensive experiments on three challenging person re identification datasets viper grid and cuhk 01 and show that dr kiss achieves new state of the art performance

semisupervised multiview distance metric learning for cartoon synthesis in image processing cartoon character classification retrieval and synthesis are critical so that cartoonists can effectively and efficiently make cartoons by reusing existing cartoon data to successfully achieve these tasks it is essential to extract visual features that comprehensively represent cartoon characters and to construct an accurate distance metric to precisely measure the dissimilarities between cartoon characters in this paper we introduce three visual features color histogram shape context and skeleton to characterize the color shape and action respectively of a cartoon character these three features are complementary to each other and each feature set is regarded as a single view however it is improper to concatenate these three features into a long vector because they have different physical properties and simply concatenating them into a high dimensional feature vector will suffer from the so called curse of dimensionality hence we propose a semisupervised multiview distance metric learning ssm dml ssm dml learns the multiview distance metrics from multiple feature sets and from the labels of unlabeled cartoon characters simultaneously under the umbrella of graph based semisupervised learning ssm dml discovers complementary characteristics of different feature sets through an alternating optimization based iterative algorithm therefore ssm dml can simultaneously accomplish cartoon character classification and dissimilarity measurement on the basis of ssm dml we develop a novel system that composes the modules of multiview cartoon character classification multiview graph based cartoon synthesis and multiview retrieval based cartoon synthesis experimental evaluations based on the three modules suggest the effectiveness of ssm dml in cartoon applications

fixed point theorems for multivalued mappings in some classes of fuzzy metic spaces abstract using the probabilistic function of noncompactness a fixed point theorem for multivalued mappings in probabilistic metric spaces is proved as an application a fixed point theorem for multivalued mappings in fuzzy metric spaces is obtained

a common fixed point theorem for r weakly commuting mappings in probabilistic spaces with nonlinear contractive conditions abstract this paper presents a common fixed point theorem for a family of r weakly commuting mappings satisfying nonlinear type contractive conditions this result improves and unifies previous results due to o regan and saadati d o regan r saadati nonlinear contraction theorems in probabilistic spaces appl math comput 195 2008 86 93 also the following results will be probabilistic versions and improvements of the results given in d w boyd j s w wong on nonlinear contractions proc am math soc 20 1969 458 464 g jungck commuting maps and fixed points am math month 83 1976 261 263 r p pant common fixed points of noncommuting mappings j math anal appl 188 1994 436 440 and many other

fixed point theorems for multivalued mappings in probabilistic metric spaces abstract in this paper we prove a fixed point theorem for multivalued mappings in probabilistic metric spaces some applications in fuzzy metric and random normed spaces are given

solving the banach fixed point principle for nonlinear contractions in probabilistic metric spaces abstract the probabilistic version of the classical banach contraction principle was proved in 1972 by sehgal and bharucha reid v m sehgal a t bharucha reid fixed points of contraction mappings on pm spaces math syst theory 6 97 102 their fixed point theorem is further generalized by many authors in the intervening years many others have proved the probabilistic versions of the other known metric fixed point theorems however the problem to prove the probabilistic versions of the very important generalization of the banach contraction principle obtained in 1969 by boyd and wong d w boyd j s w wong on nonlinear contractions proc am math soc 20 1969 458 464 who proved the fixed point theorem for a self mapping of a metric space satisfying the very general nonlinear contractive condition is unsolved in these days similarly as in the metric space case to prove a fixed point theorem for a mapping satisfying the general probabilistic nonlinear contractive condition it was necessary to find a new approach substantially different from the previous technique for cases where a mapping satisfies the probabilistic linear contraction condition introduced by sehgal and bharucha reid and further used by many authors so the problem to obtain a truthful probabilistic version of the banach fixed point principle for general nonlinear contractions existed unsolved for over 35 years we have solved this problem in this paper

the topological structure of a certain menger space in this paper we will reconsider the topological structure of menger probabilistic normed spaces briefly pn spaces under the t norm m we will prove that this topology is compatible with the topology induced by a countable and separating family of semi norms and hence the well known theorems of classical functional analysis such as the principle of uniform boundedness open mapping and closed graph theorems are valid in this context also we will meanwhile obtain a method by which one may construct easily a large class of pn spaces finally using this method we see that a certain subspace of bounded linear operators between pn spaces i e the class of strongly bounded linear operators has a natural pn structure

a fixed point theorem for multivalued mappings in probabilistic metric spaces and an application in fuzzy metric spaces in this paper we shall generalize a fixed point theorem for multivalued mappings in probabilistic metric spaces proved in j math anal appl 202 1996 433 449 as a corollary a fixed point result in menger spaces s f t where t is a strict t norm is obtained some special cases where t is a member of dombi schweizer sklar and aczel alsina families of t norms are investigated an application in fuzzy metric spaces is presented

on fuzzy metric spaces abstract in this paper we introduce the concept of a fuzzy metric space the distance between two points in a fuzzy metric space is a non negative upper semicontinuous normal and convex fuzzy number properties of fuzzy metric spaces are studied and some fixed point theorems are proved

on the yoneda completion of a quasi metric space several theories aimed at reconciling the partial order and the metric space approaches to domain theory have been presented in the literature e g flagg and kopperman theoret comput sci 177 1 1997 111 138 bonsangue et al theoret comput sci 193 1998 1 51 symth quasi uniformities reconciling domains with metric spaces lectures notes in computer science vol 298 springer berlin 1987 pp 236 253 wagner ph d thesis carnegie mellon university pittsburgh july 1994 technical report cmu cs 94 159 we focus in this paper on two of these approaches the yoneda completion of generalized metric spaces of bonsangue et al theoret comput sci 193 1998 1 51 which finds its roots in work by lawvere lawvere rend sem mat fis milano 43 1973 135 166 cf also wagner ph d thesis carnegie mellon university pittsburgh july 1994 technical report cmu cs 94 159 and which is related to early work by stoltenberg e g stoltenberg proc london math soc 3 17 1967 226 240 stoltenberg proc amer math soc 18 1967 864 867 and ferrer and gregori proc london math soc 3 49 1984 36 and the smyth completion smyth quasi uniformities reconciling domains with metric spaces lecture notes in computer science vol 298 springer berlin 1987 pp 236 253 smyth in g m reed a w roscoe r f wachter eds topology and category theory in computer science oxford university press oxford 1991 pp 207 229 smyth j london math soc 49 1994 385 400 snderhauf in m droste y gurevich eds semantics of programming languages and model theory algebra logic and applications vol 5 gordon and breach london 1993 pp 189 212 snderhauf acta math hungar 69 1995 47 54 a net version of the yoneda completion complementing the net version of the smyth completion snderhauf acta math hungar 69 1995 47 54 is given and a comparison between the two types of completion is presented the following open question is raised in bonsangue et al theoret comput sci 193 1998 1 51 an interesting question is to characterize the family of generalized metric spaces for which the yoneda completion is idempotent it contains at least all ordinary metric spaces we show that the largest class of quasi metric spaces idempotent under the yoneda completion is precisely the class of smyth completabe spaces a similar result has been obtained independently by flagg and snderhauf in flagg and snderhauf preprint available at ftp theory doc ic ac uk theory papers sunderhauf eicqf ps 2 we present an entirely new proof of the result via concrete standard techniques and compare this approach with the more abstract categorical machinery of flagg and snderhauf preprint available at ftp theory doc ic ac uk theory papers sunderhauf eicqf ps our proof is based on a new characterization of smyth completability of quasi metric spaces in terms of sequences which considerably simplifies prior characterizations for quasi uniform spaces e g snderhauf in m droste y gurevich eds semantics of programming languages and model theory algebra logic and applications vol 5 gordon and breach london 1993 pp 189 212 sunderhauf acta math hungar 69 1995 715 720 we also show that the ideal completion and hence the yoneda completion and the smyth completion are not sequentially adequate in general the study of the properties of total boundedness precompactness hereditary precompactness and compactness is motivated and we analyze the preservation of these properties under the two kinds of completion in the possible absence of idempotency

theory of traces abstract the theory of traces originated by a mazurkiewicz in 1977 is an attempt to provide a mathematical description of the behavior of concurrent systems its aim is to reconcile the sequential nature of observations of the system behavior on the one hand and the nonsequential nature of causality between the actions of the system on the other hand one can see the theory of traces to be rooted in formal string language theory with the notion of partial commutativity playing the central role alternatively one can see the theory of traces to be rooted in the theory of labeled acyclic directed graphs or even in the theory of labeled partial orders this paper attempts to present a major portion of the theory of traces in a unified way however it is not a survey in the sense that a number of new notions are introduced and a number of new results are proved although traditionally most of the development in the theory of traces follows the string language theoretic line we try to demonstrate to the reader that the graph theoretic point of view may be more appropriate the paper essentially consists of two parts the first one sections 1 through 4 is concerned with the basic theory of traces the second one section 5 presents applications of the theory of traces to the theory of the behavior of concurrent systems where the basic system model we have chosen is the condition event system introduced by c a petri

a fixed point theorem in menger space through weak compatibility this paper contains a fixed point theorem for six self maps in menger space our result generalizes and extends many known results in menger spaces and metric spaces

on contractions in probabilistic and fuzzy metric spaces in this paper by means of weakening conditions of the gauge function a new fixed point theorem for probabilistic contraction in menger probabilistic metric spaces with a t norm of h type is established this theorem improves and generalizes the recent results of iric 2010 4 jachymski 2010 12 and xiao et al 2013 25 by using the theorem we also obtain some important corollaries and the fixed point theorems for contraction in fuzzy metric spaces

common coupled fixed point results for probabilistic φ contractions in menger spaces abstract several hybrid probabilistic contractions with a gauge function are considered using the properties of the pseudo metric and the triangular norm some common coupled fixed point theorems are obtained in complete menger probabilistic metric spaces the main results are general because they do not assume any continuity or monotonicity conditions for

distance type and common fixed point theorems in menger probabilistic metric type spaces in this paper we introduce the concept of rt distance on a menger probabilistic metric type space further we prove some fixed point theorems in a complete menger probabilistic metric type space which generalizes some famous fixed point theorems

image signature highlighting sparse salient regions we introduce a simple image descriptor referred to as the image signature we show within the theoretical framework of sparse signal mixing that this quantity spatially approximates the foreground of an image we experimentally investigate whether this approximate foreground overlaps with visually conspicuous image locations by developing a saliency algorithm based on the image signature this saliency algorithm predicts human fixation points best among competitors on the bruce and tsotsos 1 benchmark data set and does so in much shorter running time in a related experiment we demonstrate with a change blindness data set that the distance between images induced by the image signature is closer to human perceptual distance than can be achieved using other saliency algorithms pixel wise or gist 2 descriptor methods

common fixed point theorems under strict contractive conditions in menger spaces abstract the main purpose of this paper is to establish some common fixed point theorems under strict contractive conditions for mappings satisfying the property e a in menger probabilistic metric spaces as applications we obtain the corresponding common fixed point theorems under strict contractive in metric spaces

linear operators in finite dimensional probabilistic normed spaces in this paper we consider strongly bounded linear operators on a finite dimensional probabilistic normed space and define the topological isomorphism between probabilistic normed spaces then we prove that every finite dimensional probabilistic normed space which is a topological vector space is complete

generalization of shadows and fixed point theorems for fuzzy sets in this paper we define a fuzzy set concerning shadows without assuming the existence of the metric projection and extend a well known result in a hilbert space to that in a normed linear space we shall observe that the fuzzy set presented here is in essence a generalization of shadows further we study fuzzy mappings in the framework of fixed point theory we first prove two theorems extending nadler s fixed point theorem lots of fixed point theorems for fuzzy mappings have been proved however the method used here is completely different from those in the previous results next we prove a theorem by applying fan s fixed point theorem and conversely we show that this is a generalization of this theorem

multiple metric learning based on bar shape descriptor for person re identification abstract the robust structural feature extraction and similarity measure play critical roles in person re identification this paper presents a novel algorithm named multiple metric learning based on bar shape descriptor mmlbd for person re identification specifically we first propose a new multiple bar shape descriptor that can take full account of the spatial correlation between the center points and their adjacent points on different directions it captures further histogram features based on a novel color difference weight factors with an overlapping sliding window which can depict the local variations and consistency in the whole image the similarity and dissimilarity of samples are used to train the weight factor of features and an optimal subspace could be obtained at the same time next we provide an effective multiple metric learning method fusing two channel bar shape structural features via the optimal similarity pairwise measure obtained by a dissimilarity matrix this measure can fully mine the discriminative information and eliminate redundancy in the similar features which make the mmlbd simple and effective finally evaluation experiments on the i lids caviar4reid and ward data sets are carried out which compare the proposed mmlbd with the corresponding methods experimental results demonstrate that the mmlbd is more effective and robust against visual appearance variations

a partial trace semantics for petri nets abstract we introduce the notion of partial trace a partial trace is an equivalence class of some labelled partial orders over a dependence alphabet sd partial traces arise in a natural way by the synchronization of semi traces they form a monoid which is shown to be free partially commutative we prove an embedding theorem which shows that any partial trace has a canonical representation as a tuple of words we then apply this concept to petri nets we define the behavior of a p t system in terms of partial traces we consider local morphisms between petri nets and we show how this relates to the partial trace behavior in particular we obtain the desired result that the partial trace behavior of a synchronized system is the synchronization of its local behavior

applications of the complexity space to the general probabilistic divide and conquer algorithms abstract schellekens m schellekens the smyth completion a common foundation for denotational semantics and complexity analysis in proc mfps 11 in electron notes theor comput sci vol 1 1995 pp 535 556 and romaguera and schellekens s romaguera m schellekens quasi metric properties of complexity spaces topology appl 98 1999 311 322 introduced a topological foundation to obtain complexity results through the application of semantic techniques to divide and conquer algorithms this involved the fact that the complexity quasi metric space is smyth complete and the use of a version of the banach fixed point theorem and improver functionals to further bridge the gap between semantics and complexity we show here that these techniques of analysis based on the theory of complexity spaces extend to general probabilistic divide and conquer schema discussed by flajolet p flajolet analytic analysis of algorithms in w kuich ed 19th internat colloq icalp 92 vienna july 1992 automata languages and programming in lecture notes in comput sci vol 623 1992 pp 186 210 in particular we obtain a general method which is useful to show that for several recurrence equations based on the recursive structure of general probabilistic divide and conquer algorithms the associated functionals have a unique fixed point which is the solution for the corresponding recurrence equation

multiresolution gray scale and rotation invariant texture classification with local binary patterns presents a theoretically very simple yet efficient multiresolution approach to gray scale and rotation invariant texture classification based on local binary patterns and nonparametric discrimination of sample and prototype distributions the method is based on recognizing that certain local binary patterns termed uniform are fundamental properties of local image texture and their occurrence histogram is proven to be a very powerful texture feature we derive a generalized gray scale and rotation invariant operator presentation that allows for detecting the uniform patterns for any quantization of the angular space and for any spatial resolution and presents a method for combining multiple operators for multiresolution analysis the proposed approach is very robust in terms of gray scale variations since the operator is by definition invariant against any monotonic transformation of the gray scale another advantage is computational simplicity as the operator can be realized with a few operations in a small neighborhood and a lookup table experimental results demonstrate that good discrimination can be achieved with the occurrence statistics of simple rotation invariant local binary patterns

coupled coincidence point theorems under contractive conditions in partially ordered probabilistic metric spaces abstract in this paper we introduce the concept of a mixed g monotone mapping and prove coupled coincidence and coupled common fixed point theorems under contractive conditions for self maps in partially ordered complete probabilistic metric spaces

generalized vector complementarity problem in fuzzy environment abstract this paper is devoted to introduce and study a new class of generalized vector complementarity problems gvcp for short and generalized vector variational inequalities gvvi for short in fuzzy environment under suitable conditions we prove the equivalence between gvcp and gvvi in banach spaces then without any monotonicity assumption we apply kkm technique to establish an existence theorem of solutions for gvvi finally we show that the solution set of gvcp is nonempty and closed

on quasi metric aggregation functions and fixed point theorems the problem of how to merge by means of a function a family of metrics into a single one was studied deeply by j borsik and j dobos on a product of metric spaces math slovaca31 1981 193 205 motivated by the utility of quasi metrics in computer science the borsik and dobos study was extended to the quasi metric context in such a way that a general description of how to combine through a function a family of quasi metrics in order to obtain a single one as output was provided by g mayor and o valero aggregation of asymmetric distances in computer science inform sci 180 2010 803 812 in this paper inspired by the fact that fixed point theory provides an efficient tool in many fields of applied sciences we have proved fixed point theorems for a new type of contractions that we have called projective f contractions defined between quasi metric spaces that have been obtained via the so called quasi metric aggregation functions moreover we show that the new fixed point results are useful to discuss on the one hand the complexity of a collection of recursive programs whose running times of computing hold a coupled system of recurrence equations and on the other hand to analyze simultaneously the complexity and the correctness of recursive algorithms that perform a computation by means of a recursive denotational specification

multivalued generalizations of probabilistic contractions we generalize some well known fixed point theorems for probabilistic contractions to multivalued contractions the contraction maps are considered in generalized menger spaces

characterizations of metrizable topological vector spaces and their asymmetric generalizations in terms of fuzzy quasi norms we obtain characterizations of those paratopological vector spaces that are quasi metrizable locally bounded quasi metrizable locally convex and quasi normable respectively in terms of appropriate kinds of fuzzy quasi norms characterizations of distinguished kinds of metrizable topological vector spaces some of them known already are deduced as particular cases of our approach

matching shape sequences in video with applications in human movement analysis we present an approach for comparing two sequences of deforming shapes using both parametric models and nonparametric methods in our approach kendall s definition of shape is used for feature extraction since the shape feature rests on a non euclidean manifold we propose parametric models like the autoregressive model and autoregressive moving average model on the tangent space and demonstrate the ability of these models to capture the nature of shape deformations using experiments on gait based human recognition the nonparametric model is based on dynamic time warping we suggest a modification of the dynamic time warping algorithm to include the nature of the non euclidean space in which the shape deformations take place we also show the efficacy of this algorithm by its application to gait based human recognition we exploit the shape deformations of a person s silhouette as a discriminating feature and provide recognition results using the nonparametric model our analysis leads to some interesting observations on the role of shape and kinematics in automated gait based person authentication

fixed point theorems for fuzzy mappings abstract this paper presents some new fixed point theorems for fuzzy mappings the results given in this paper improve and extend some recent results

probabilistic fractals and attractors in menger spaces abstract probabilistic fractals are considered as self similar sets for contraction mappings in hyperspaces of the menger probabilistic metric spaces the completeness of hyperspaces of all closed or closed and bounded or compact nonempty subsets with respect to the probabilistic hausdorff metric is studied in some general conditions of triangular norm using the properties of hyperspaces and triangular norms of h type several existence results of attractors are obtained for a finite family and a countable family of probabilistic nonlinear contractions respectively our results are generalizations in many aspects

couple fixed point theorems for nonlinear contractions in cone metric spaces the notion of coupled fixed point is introduced by bhaskar and lakshmikantham 2006 in 13 in this manuscript some results of lakshmikantham and ciric 2009 in 5 are extended to the class of cone metric spaces

kernelized saliency based person re identification through multiple metric learning person re identification in a non overlapping multi camera scenario is an open and interesting challenge while the task can hardly be completed by machines we as humans are inherently able to sample those relevant persons details that allow us to correctly solve the problem in a fraction of a second thus knowing where a human might fixate to recognize a person is of paramount interest for re identification inspired by the human gazing capabilities we want to identify the salient regions of a person appearance to tackle the problem toward this objective we introduce the following main contributions a kernelized graph based approach is used to detect the salient regions of a person appearance later used as a weighting tool in the feature extraction process the proposed person representation combines visual features either considering or not the saliency these are then exploited in a pairwise based multiple metric learning framework finally the non euclidean metrics that have been separately learned for each feature are fused to re identify a person the proposed kernelized saliency based person re identification through multiple metric learning has been evaluated on four publicly available benchmark data sets to show its superior performance over the state of the art approaches e g it achieves a rank 1 correct recognition rate of 42 41 on the viper data set

on fixed degree theorems for fuzzy mappings in menger pm spaces in this paper we establish a new common fixed degree theorem for a sequence of fuzzy mappings in menger pm spaces as an immediate consequence of this theorem we obtain an improvement of a corresponding result of chang et al fuzzy sets and systems 87 1997 325 334 in addition we also obtain some fixed degree and fixed point theorems for fuzzy mappings in fuzzy metric spaces our results unify and generalize the results of heilpern j math anal appl 83 1981 566 569 butnariu fuzzy sets and systems 7 1982 191 207 hadzic fuzzy sets and systems 29 1989 115 125 fang fuzzy sets and systems 48 1992 391 395 lee et al fuzzy sets and systems 61 1994 309 312 j fuzzy math 2 1994 859 870 and chang et al math japon 40 1994 289 293 fuzzy sets and systems 87 1997 325 334

on the normability of generalized serstnev pn spaces probabilistic normed spaces have been redefined by c alsina b schweizer and a sklar but even today whether the generalized serstnev pn space is normable or not is still an open question in this paper through applying kolmogorov s theorem we will give several sufficient conditions under which many generalized serstnev pn spaces are normable as the application of our results we will give two examples which are normable generalized serstnev pn space but not serstnev space

some topologies on a serstnev probabilistic normed space abstract in this paper we will introduce two other topologies coarser than the so called strong topology on a class of serstnev probabilistic normed spaces and obtain some important properties of these topologies we will show that under the first topology denoted by 0 our probabilistic normed space is decomposable into the topological direct sum of a normable subspace and the subspace of probably null elements under the second topology which is in fact the inductive limit topology of a family of locally convex topologies the dual space becomes a locally convex topological vector space

visual saliency based on scale space analysis in the frequency domain we address the issue of visual saliency from three perspectives first we consider saliency detection as a frequency domain analysis problem second we achieve this by employing the concept of nonsaliency third we simultaneously consider the detection of salient regions of different size the paper proposes a new bottom up paradigm for detecting visual saliency characterized by a scale space analysis of the amplitude spectrum of natural images we show that the convolution of the image amplitude spectrum with a low pass gaussian kernel of an appropriate scale is equivalent to an image saliency detector the saliency map is obtained by reconstructing the 2d signal using the original phase and the amplitude spectrum filtered at a scale selected by minimizing saliency map entropy a hypercomplex fourier transform performs the analysis in the frequency domain using available databases we demonstrate experimentally that the proposed model can predict human fixation data we also introduce a new image database and use it to show that the saliency detector can highlight both small and large salient regions as well as inhibit repeated distractors in cluttered images in addition we show that it is able to predict salient regions on which people focus their attention

common fixed point theorems of compatible and weakly compatible maps in menger spaces abstract in this paper we prove some new common fixed point theorems for compatible and weakly compatible self maps on menger space under contractive conditions our results improve and generalize the results of singh and jain b singh s jain a fixed point theorem in menger space through weak compatibility j math anal appl 301 2005 439 448 razani and shirdaryazdi a razani m shirdaryazdi a common fixed point theorem of compatible maps in menger space chaos solitons fractals 32 2007 26 34 and others

a coupled coincidence point result in partially ordered metric spaces for compatible mappings abstract in this paper we introduce the notion of compatibility of mappings in a partially ordered metric space and use this notion to establish a coupled coincidence point result our work extends the work of bhaskar and lakshmikantham t gnana bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal tma 65 2006 1379 1393 an example is also given

convolutional covariance features conception integration and performance in person re identification abstract this paper introduces a novel type of features based on covariance descriptors the convolutional covariance features ccf differently from the traditional and handcrafted way to obtain covariance descriptors ccf is computed from adaptive and trainable features which come from a coarse to fine transfer learning cfl strategy cfl provides a generic to specific knowledge and noise invariant information for person re identification after training the deep features convolutional and flat features are extracted from respectively intermediate and top layers of a hybrid deep network intermediate layer features are then wrapped in covariance matrices composing the so called ccf which are integrated to the top layer features called here flat features integration of ccf and flat features demonstrated to improve the proposed person re identification in comparison with the use of the component features alone our person re identification method achieved the best top 1 performance when compared with other 18 state of the art methods over viper i lids cuhk01 and cuhk03 data sets the compared methods are based on deep learning covariance descriptors or handcrafted features and similarity functions

nonlinear coupled coincidence and coupled fixed point theorems for not necessary commutative contractive mappings in partially ordered probabilistic metric spaces in this paper we introduce the notion of compatibility of mappings in partially ordered probabilistic metric spaces and use this notion to establish a coupled coincidence point result very recently hu and ma xin qi hu xiao yan ma coupled coincidence point theorems under contractive conditions in partially ordered probabilistic metric spaces nonlinear anal 74 2011 6451 6458 proved coupled coincidence point theorems for commuting mappings in partially ordered probabilistic metric spaces in this paper we proved results of hu and ma under a different set of conditions precisely we establish our results by assuming that two mappings on a partially ordered probabilistic metric spaces are compatible not necessary commutative and satisfy a more general contractive condition than the contractive condition in the main theorem of hu and ma our results improve and extend a coupled coincidence point theorem due to hu and ma as well as a coupled fixed point theorem due to bhaskar and lakshmikantham t g bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal 65 2006 1379 1393 an example is given to support our result

partial commutations and faithful rational transductions abstract we study the operation of partial commutation in connection with other operations such as partitioned commutation twin shuffle intersection and faithful rational transductions from that study we get a very simple characterization for the following families of languages multi reset bnp and q the family of quasirealtime languages

coincidence point theorems in probabilistic and fuzzy metric spaces in this paper we prove some new coincidence point theorems for a hybrid pair of single and multi valued mappings under more generalized contractive conditions in menger spaces and generalized menger spaces our results can be applied to the theory of the fuzzy metric spaces by relaxing some conditions several recent results given by zikic dos enovic mihet and ghaemi and razani are extended

coupled fixed point theorems for a generalized meir keeler contraction in partially ordered metric spaces abstract let x be a non empty set and f x x x be a given mapping an element x y x x is said to be a coupled fixed point of the mapping f if f x y x and f y x y in this paper we consider the case when x is a complete metric space endowed with a partial order we define generalized meir keeler type functions and we prove some coupled fixed point theorems under a generalized meir keeler contractive condition some applications of our obtained results are given the presented theorems extend and complement the recent fixed point theorems due to bhaskar and lakshmikantham t gnana bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal 65 2006 1379 1393

on fixed point theorems in fuzzy metric spaces we give fixed point theorems for complete fuzzy metric spaces in the sense of george and veeramani and also for kramosil and michalek s fuzzy metric spaces which are complete in grabiec s sense

reidentification by relative distance comparison matching people across nonoverlapping camera views at different locations and different times known as person reidentification is both a hard and important problem for associating behavior of people observed in a large distributed space over a prolonged period of time person reidentification is fundamentally challenging because of the large visual appearance changes caused by variations in view angle lighting background clutter and occlusion to address these challenges most previous approaches aim to model and extract distinctive and reliable visual features however seeking an optimal and robust similarity measure that quantifies a wide range of features against realistic viewing conditions from a distance is still an open and unsolved problem for person reidentification in this paper we formulate person reidentification as a relative distance comparison rdc learning problem in order to learn the optimal similarity measure between a pair of person images this approach avoids treating all features indiscriminately and does not assume the existence of some universally distinctive and reliable features to that end a novel relative distance comparison model is introduced the model is formulated to maximize the likelihood of a pair of true matches having a relatively smaller distance than that of a wrong match pair in a soft discriminant manner moreover in order to maintain the tractability of the model in large scale learning we further develop an ensemble rdc model extensive experiments on three publicly available benchmarking datasets are carried out to demonstrate the clear superiority of the proposed rdc models over related popular person reidentification techniques the results also show that the new rdc models are more robust against visual appearance changes and less susceptible to model overfitting compared to other related existing models

on fixed point theorems in fuzzy metric spaces abstract the purpose of this paper is to give some new fixed point theorems for contractive type mappings in fuzzy metric spaces the results presented improve and generalize some recent results

fixed point theorems for fuzzy mappings abstract in this paper we prove fixed point theorems for fuzzy mappings satisfying contractive type conditions and a rational inequality in complete metric spaces

ordinal margin metric learning and its extension for cross distribution image data propose a novel ordinal margin metric learning ormml by separating the data with large margins and making them distributed in order extend ormml to cope with cross distribution application scenarios named cd ormml extensively demonstrate the superiority of the proposed metric learning methods to related state of the art methods in machine learning and computer vision fields a wide range of applications such as human age estimation and head pose recognition are related to ordinal data in which there exists an order relationship to perform such ordinal estimations in a desired metric space in this paper we first propose a novel ordinal margin metric learning ormml method by separating the data classes with a sequence of margins which makes the classes distribute orderly in the learned metric space then to cope with more realistic scenarios where the data are sampled with each class across multiple distributions we present a cross distribution variant of ormml coined as cd ormml by maximizing the correlation between distributions within each class when conducting metric learning finally extensive experiments on synthetic and publicly available image datasets demonstrate the superiority of the proposed methods in performance to the state of the art methods

fuzzy contractive maps and fuzzy fixed points this paper presents a variety of fuzzy fixed point theorems for contractive type maps our theory can be derived directly from results in the literature related to multivalued contractive maps with closed values this observation seems to have been overlooked in the literature