direct and inverse computation of jacobi matrices of infinite iterated function systems we introduce a new set of algorithms to compute the jacobi matrices associated with invariant measures of infinite iterated function systems composed of one dimensional homogeneous affine maps we demonstrate their utility in the study of theoretical problems like the conjectured almost periodicity of such jacobi matrices the singularity of the measures and the logarithmic capacity of their support since our technique is based on a reversible transformation between pairs of jacobi matrices it can also be applied to solve an inverse approximation problem the proposed algorithms are tested in significant highly sensitive cases they perform in a stable fashion and can reliably compute jacobi matrices of large order

fixed point theory for self maps between frechet spaces abstract using krasnoselskii s fixed point theorem in a cone we present a new fixed point theory for multivalued self maps between frechet spaces our analysis relies on a diagonal process and a result on hemicompact maps due to k k tan and x z yuan 1994 j math anal appl 185 378 390 an application is given to illustrate the theory

the picard contraction mapping method for the parameter inversion of reaction diffusion systems an inverse problem is to determine unknown causes based on observation of their effects such problems often arise in scientific research and engineering practice in this paper we present a parameter inversion method for a class of reaction diffusion systems by the use of the picard contraction mapping we firstly establish an approximate differential equation model which corresponds to the given reaction diffusion system and discuss the contractivity of the picard mapping associated with the approximate model then we provide an algorithm for recovering parameters of the reaction diffusion system based on the collage theorem numerical tests show that the proposed method is efficient

random fixed point theorems for various classes of 1 set contractive maps in banach spaces abstract various random fixed point theorems for different classes of 1 set contractive random operator are proved the class of 1 set contractive random operators includes condensing and nonexpansive random operators it also includes semicontractive type random operators and locally almost nonexpansive random operators thus results due to s itoh j math anal appl 67 1979 261 273 t c lin proc amer math soc 103 1988 1129 1135 proc amer math soc 123 1995 1167 1176 and h k xu proc amer math soc 110 1990 495 500 are either extended or improved

generalized self similarity abstract we prove the existence of l pfunctions satisfying a kind of self similarity condition this is achieved by solving a functional equation by means of the construction of a contractive operator on an appropriate functional space the solution a fixed point of the operator can be obtained by an iterative process making this model very suitable to use in applications such as fractal image and signal compression on the other hand this generalized self similarity equation includes matrix refinement equations of the typef x ckf ax k which are central in the construction of wavelets and multiwavelets the results of this paper will therefore yield conditions for the existence of l p refinable functions in a very general setting

distances between fuzzy measures through associated probabilities some applications in a recent paper a method to study fuzzy measures by means of certain sets of associated probabilities has been developed in this paper distances in the set of fuzzy measures are defined trough distances between the associated probabilities finally some applications of these distances to measure the uncertainty and specificity of fuzzy measures as well as to approximate fuzzy measures are considered

anzellotti s pairing theory and the gauss green theorem abstract in this paper we obtain a very general gauss green formula for weakly differentiable functions and sets of finite perimeter this result is obtained by revisiting anzellotti s pairing theory and by characterizing the measure pairing a d u when a is a bounded divergence measure vector field and u is a bounded function of bounded variation

cauchy fluxes and gauss green formulas for divergence measure fields over general open sets we establish the interior and exterior gauss green formulas for divergence measure fields in lp over general open sets motivated by the rigorous mathematical formulation of the physical principle of balance law via the cauchy flux in the axiomatic foundation for continuum mechanics allowing discontinuities and singularities the method based on a distance function allows us to give a representation of the interior resp exterior normal trace of the field on the boundary of any given open set as the limit of classical normal traces over the boundaries of interior resp exterior smooth approximations of the open set in the particular case of open sets with a continuous boundary the approximating smooth sets can explicitly be characterized by using a regularized distance we also show that any open set with lipschitz boundary has a regular lipschitz deformable boundary from the interior in addition some new product rules for divergence measure fields and suitable scalar functions are presented and the connection between these product rules and the representation of the normal trace of the field as a radon measure is explored with these formulas to hand we introduce the notion of cauchy fluxes as functionals defined on the boundaries of general bounded open sets for the rigorous mathematical formulation of the physical principle of balance law and show that the cauchy fluxes can be represented by corresponding divergence measure fields

two integrals and some modified versions critical remarks the aim of this paper is to discuss different constructions of integrals sections 3 and 4 based on decomposable measures section 1 according to the classification of the continuous t conorms in essentially two types namely v and archimedean t conorms there exist mainly two types of integrals namely the constructions of sugeno section 3 and of weber section 4 further constructions corresponding to the archimedean case result to be special cases or not well defined section 4 in all cases a crucial property is some restricted distribution law for the pair with an appropriate operation section 2 some applications shall illustrate the use of the two integrals section 5

divergence measure fields and hyperbolic conservation laws we analyze a class of l infty vector fields called divergence measure fields we establish the gauss green formula the normal traces over subsets of lipschitz boundaries and the product rule for this class of l infty fields then we apply this theory to analyze l infty entropy solutions of initial boundary value problems for hyperbolic conservation laws and to study the ways in which the solutions assume their initial and boundary data the examples of conservation laws include multidimensional scalar equations the system of nonlinear elasticity and a class of m x m systems with affine characteristic hypersurfaces the analysis in l infty also extends to l p

fractal image denoising over the past decade there has been significant interest in fractal coding for the purpose of image compression however applications of fractal based coding to other aspects of image processing have received little attention we propose a fractal based method to enhance and restore a noisy image if the noisy image is simply fractally coded a significant amount of the noise is suppressed however one can go a step further and estimate the fractal code of the original noise free image from that of the noisy image based upon a knowledge or estimate of the variance of the noise assumed to be zero mean stationary and gaussian the resulting fractal code yields a significantly enhanced and restored representation of the original noisy image the enhancement is consistent with the human visual system where extra smoothing is performed in flat and low activity regions and a lower degree of smoothing is performed near high frequency components e g edges of the image we find that for significant noise variance spl sigma spl ges 20 the fractal based scheme yields results that are generally better than those obtained by the lee filter which uses a localized first order filtering process similar to fractal schemes we also show that the lee filter and the fractal method are closely related

some random approximation theorems with applications fan 8 proved a very interesting theorem which provides a tool to study xed point theory in connection with best approximation various aspects of that theorem have been studied by fan 9 ha 10 singh and watson 22 lin 14 lin and yen 16 and many others fan s theorem has been of great importance in nonlinear analysis approximation theory game theory and minimax theorems the study of random approximations and random xed points have been a very active area of research in probabilistic functional analysis in the last decade see sehgal and waters 21 sehgal and singh 20 papageorgiou 18 lin 15 xu 25 tan and yuan 23 24 and beg and shahzad 1 4 most random xed point theorems in banach spaces deal with condensing or nonexpansive random operators what about the random operators which are neither of the above cases the interesting case would be a 1 set contractive random operator the class of 1 set contractive random operators includes condensing and nonexpansive random operators besides it also includes other important random operators such as semicontractive random operators and lane locally almost nonexpansive random operators recently beg and shahzad 3 studied these random operators in details and gave many results regarding random approximations and random

on the solutions to 1 laplacian equation with l1 data in the present paper we study the behaviour as p goes to 1 of the renormalized solutions to the problems 0 1 div up p 2 up fin up 0on where p 1 is a bounded open set of rn n 2 with lipschitz boundary and f belongs to l1 we prove that these renormalized solutions pointwise converge up to subsequences to a function u with a suitable definition of solution we also prove that u is a solution to a limit problem moreover we analyze the situation occurring when more regular data f are considered

stochastic perturbation of dynamical systems the weak convergence of measures in this paper we consider the asymptotic behaviour of randomly perturbed discrete dynamical systems we treat this problem by examining the evolution of the corresponding sequences of distributions we show that an average contractive property is sufficient to ensure the weak convergence of the sequence of distributions to a unique stationary measure

approximations of fractal sets abstract five approximations of fractal sets a are compared the first three were described by hutchinson barnsley demko and williams respectively two new other approximations are still efficient in all circumstances for any algorithm error estimates in the approximations are found numerical comparisons are also done through classical examples of attractors in the plane

stochastic convergence uniform integrability and convergence in mean on fuzzy measure spaces the paper deals with the convergence of sequences of measurable functions on fuzzy measure spaces a classical result that relates the uniform integrability plus stochastic convergence with convergence in mean is extended to this case where the additivity property of measures is not required we also investigate the sufficient and necessary conditions that fuzzy measures must satisfy in the dominated convergence theorem

the gauss green theorem in stratified groups abstract we lay the foundations for a theory of divergence measure fields in noncommutative stratified nilpotent lie groups such vector fields form a new family of function spaces which generalize in a sense the bv fields they provide the most general setting to establish gauss green formulas for vector fields of low regularity on sets of finite perimeter we show several properties of divergence measure fields in stratified groups ultimately achieving the related gauss green theorem

random fixed point equations and inverse problems using collage method for contraction mappings abstract in this paper we are interested in the direct and inverse problems for the following class of random fixed point equations t w x w x w where t x x is a given operator is a probability space and x is a polish metric space the inverse problem is solved by recourse to the collage theorem for contractive maps we then consider two applications i random integral equations and ii random iterated function systems with greyscale maps rifsm for which noise is added to the classical ifsm

coincidence points generalized i nonexpansive multimaps and applications we establish coincidence point results for multimaps satisfying generalized i nonexpansive type conditions several invariant approximation results are obtained as applications a random coincidence point result is also proved and as applications random invariant approximation results are obtained our results unify extend and complement several well known results

existence results for nonlinear integral equations the schauder tychonoff theorem in locally convex topological hausdorff spaces and a nonlinear alternative of leray schauder type are used to establish some existence results for volterra and hammerstein integral equations

a fixed point theorem for condensing operators and applications to hammerstein integral equations in banach spaces abstract we prove a fixed point theorem of furi pera type for condensing operators this will then be used to establish the existence of solutions to certain integral equations of hammerstein type in banach spaces

a parametric level set based collage method for an inverse problem in elliptic partial differential equations in this work based on the collage theorem we develop a new numerical approach to reconstruct the locations of discontinuity of the conduction coefficient in elliptic partial differential equation

cone compression and expansion fixed point theorems in frechet spaces with applications abstract new fixed point theory for multivalued maps between frechet spaces is presented applications are given to illustrate how the theory can be applied in practice

fixed point theory for admissible multimaps defined on closed subsets of frechet spaces abstract this paper presents new fixed point results for a general class of maps defined on frechet spaces our results in particular apply to kakutani acyclic o neill approximable admissible with respect to gorniewicz and u c maps

novel techniques in parameter estimation for fractional dynamical models arising from biological systems in recent years both parameter estimation and fractional calculus have attracted a considerable interest parameter estimation of the fractional dynamical models is a new topic in this paper we consider novel techniques for parameter estimation of fractional nonlinear dynamical models in systems biology first a computationally effective fractional predictor corrector method is proposed for simulating fractional complex dynamical models second we convert the parameter estimation of fractional complex dynamical models into a minimization problem of the unknown parameters third a modified hybrid simplex search mhss and a particle swarm optimization pso is proposed finally these techniques are applied to a dynamical model of competence induction in a cell with measurement error and noisy data some numerical results are given that demonstrate the effectiveness of the theoretical analysis

contractive multifunctions fixed point inclusions and iterated multifunction systems abstract we study the properties of multifunction operators that are contractive in the covitz nadler sense in this situation such operators t possess fixed points satisfying the relation x t x we introduce an iterative method involving projections that guarantees convergence from any starting point x 0 x to a point x x t the set of all fixed points of a multifunction operator t we also prove a continuity result for fixed point sets x t as well as a generalized collage theorem for contractive multifunctions these results can then be used to solve inverse problems involving contractive multifunctions two applications of contractive multifunctions are introduced i integral inclusions and ii iterated multifunction systems

on the chain rule formulas for divergences and applications to conservation laws abstract in this paper we prove a nonautonomous chain rule formula for the distributional divergence of the composite function v x b x u x where b t is a divergence measure vector field and u is a function of bounded variation as an application we prove a uniqueness result for scalar conservation laws with discontinuous flux

a technique for image magnification using partitioned iterative function system abstract a new technique for image magnification using the theory of fractals is proposed the technique is designed assuming self transformability property of images in particular the magnification task is performed using the fractal code of the image instead of the original one resulting in a reduction in memory requirement to generate the fractal codes genetic algorithm with elitist model is used which greatly decreases the search for finding self similarities in the given image the article presents both theory and implementation of the proposed method a simple distortion measure scheme and a similarity criterion based on just noticeable difference have also been proposed to judge the image quality of the magnified image comparison with one of the most popular magnification techniques the nearest neighbor technique is made

an automatization of barnsley s algorithm for the inverse problem of iterated function systems we present an automatization of barnsley s manual algorithm for the solution of the inverse problem of iterated function systems ifss the problem is to retrieve the number of mappings and the parameters of an ifs from a digital binary image approximating the attractor induced by the ifs m f barnsley et al described a way to solve manually the inverse problem by identifying the fragments of which the collage is composed and then computing the parameters of the mappings barnsley et al proc nat acad sci usa vol 83 p 1975 7 1986 barnsley fractals everywhere academic 1988 barnsley and hurd l fractal image compression a k peters 1992 the automatic algorithm searches through a finite set of points in the parameter space determining a set of affine mappings the algorithm uses the collage theorem and the hausdorff metric the inverse problem of ifss is related to the image coding of binary images if the number of mappings and the parameters of an ifs with not too many mappings could be obtained from a binary image then this would give an efficient representation of the image it is shown that the inverse problem solved by the automatic algorithm has a solution and some experiments show that the automatic algorithm is able to retrieve an ifs including the number of mappings from a digital binary image approximating the attractor induced by the ifs

random fixed points of k set and pseudo contractive random maps abstract let be a measurable space x and y separable banach spaces and c a weakly compact subset of x let f c y and t c y be continuous random operators then the deterministic solvability of the equation f x t x 0 x c implies the stochastic solvability of it provided that f t is demiclosed at zero and t c is bounded for each as applications random fixed points of various types of pseudo contractive and k set contractive random operators are obtained

a generalized collage method based upon the lax milgram functional for solving boundary value inverse problems abstract some inverse problems can be cast as approximating a given target function perhaps the interpolation of observational data points by the fixed points of an operator equation the collage method refers to the solution strategy of bounding above the true approximation error by a more readily minimizable quantity in this paper we present a collage method for solving inverse problems for boundary value problems the approach is based upon the lax milgram representation theorem for applications we focus on one and two dimensional steady state reaction diffusion equations

using iterated function systems to model discrete sequences two iterated function system ifs models are explored for the representation of single valued discrete time sequences the self affine fractal model and the piecewise self affine fractal model algorithms are presented one of which is suitable for a multiprocessor implementation for identification of the parameters of each model applications of these models to a variety of data types are given where signal to noise ratios are presented quantization effects of the model parameters are investigated and compression ratios are computed

choquet integral and fuzzy measures on locally compact space the concept of outer regular fuzzy measures is proposed and it is shown that a functional of certain type on the cone of positive continuous functions with compact supports is represented as a choquet integral with respect to a outer regular fuzzy measure it is also shown that the choquet integral of positive continuous functions with compact supports is represented as a lebesgue integral with the same integrands this representation is a generalization of certain previous results of others which are useful for computation of the upper and lower expected value

an extension of the pairing theory between divergence measure fields and bv functions abstract in this paper we introduce a nonlinear version of the notion of anzellotti s pairing between divergence measure vector fields and functions of bounded variation motivated by possible applications to evolutionary quasilinear problems as a consequence of our analysis we prove a generalized gauss green formula

random fixed points for several classes of 1 ball contractive and 1 set contractive random maps a general random fixed point theorem for continuous random operators is proved as applications a number of random fixed points theorems for various classes of 1 set and 1 ball contractive random operators e g operators of contractive type with compact or completely continuous perturbations operators of semicontractive type etc are derived our results unify and extend most of the known random fixed points theorems 1991 ams subject classification 47h10 60h25

convex duality and uniqueness for bv minimizers we are concerned with the dirichlet minimization problem for variational integrals with linear growth in the existence theory for minimizers one commonly considers a generalized formulation in the space of functions of bounded variation while on the other hand the dual problem in the classical sense of convex analysis is a maximization problem in the space of divergence free bounded vector elds in this paper we characterize extremals of the generalized and the dual problem by pointwise extremality relations and we discuss uniqueness issues for both kinds of solutions our approach is suciently general to cover arbitrary dimensions non smooth integrands and unbounded irregular domains msc 2010 49k20 49n15 primary 26b25 26b30 46g10 secondary

galerkin method for constrained variational equations and a collage based approach to related inverse problems for a general variational equation with constraints we present both the stability of the corresponding galerkin method and a collage theorem for a related inverse problem in addition we demonstrate the applicability of the results by considering forward and inverse boundary value problems of some linear impulsive differential equations

random fixed points of set valued maps some random fixed point theorems for set valued random operators under very mild conditions are established some recent results of o regan proc amer math soc 126 1998 3045 3053 and computers math applic 35 1998 27 34 are improved significantly the discussion in this paper underlines in addition to generality the unifying aspects of our result

an inductive learning procedure to identify fuzzy systems abstract in many real cases a system may not be described by a functional input output description and the only way to describe it is through a finite set of fuzzy rules even in some cases where exact identification is possible looking for that rule description may be useful for the sake of ease and effectiveness the automatic identification of a system through the analysis of an input output data set is the aim of this work in order to identify a system from raw data obtained in repeated instances of its own system the frequency of appearance of some kind of patterns may be particularly interesting nevertheless when the base domain is fuzzy and the data can be crisp statistical methods are not very appropriate and it is necessary to study a new model for frequencies on fuzzy domains the proposed model for identifying systems is based on this definition

ifs imaging beyond compression abstract historically most research in fractal image coding focused on its compression capabilities seeking to obtain the best domain range block matching with the minimal amount of fractal code in the course of these investigations it was implicitly known yet perhaps not fully investigated that a number of domain image subblocks will approximate a given range image subblock almost as well as the optimal domain subblock selected by collage coding recently we have presented a simple mathematical model of image self similarity and a series of computer experiments that examine the self similarity of natural images under contractive affine greyscale maps s alexander e vrscay s tsurumi a simple general model for the affine self similarity of images in a campilho m karnel eds iciar in lecture notes in computer science vol 5112 springer verlag 2008 pp 192 203 s alexander multiscale methods in image modelling and image processing ph d thesis dept of applied mathematics university of waterloo 2005 we demonstrated that typical natural images have large numbers of such maps that closely approximate all areas i e range subblock of the image in the present work some implications of this are explored a novel ifs type fractal operator with overlapping maps ifsom is presented application of this technique in a multiscale manner is demonstrated to have denoising performance comparable to current state of the art methods extensions of this preliminary work are discussed

fractal block coding a functional approach for image and signal processing in this paper we show how the generalized self similarity model introduced by cabrelli et al in 1 can be used for the coding and reconstruction of digital signals and images we also prove how the block coding techniques introduced by jacquin 2 for measures flt naturally into this functional model allowing us to take advantage of local redundancy of the images as well as to fully automate the encoding and decoding process c

fixed point theorems for countably condensing maps on frechet spaces abstract new fixed point results for countably condensing operators defined on frechet spaces are presented applications to integral inclusions are also discussed

inverse problems in fractal construction moment method solution abstract the inverse problem for several classes of fractals in one and two dimensions can be profitably solved via the application of the classical theory of moments this new perspective leads to important results on the reconstruction process when only a finite number of moments of the fractal measures are known while discussing the rigorous aspects of the theory we also implement it via efficient numerical algorithms

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

region based fractal image compression using heuristic search presents work carried out on fractal or attractor image compression the approach relies on the assumption that image redundancy can be efficiently exploited through self transformability the algorithms described utilize a novel region based partition of the image that greatly increases the compression ratios achieved over traditional block based partitionings due to the large search spaces involved heuristic algorithms are used to construct these region based transformations results for three different heuristic algorithms are given the results show that the region based system achieves almost double the compression ratio of the simple block based system at a similar decompressed image quality for the lena image compression ratios of 41 1 can be achieved at a psnr of 26 56 db

using the collage method to solve odes inverse problems with multiple data sets abstract we consider inverse problems for ordinary differential equations odes where multiple noisy observational data sets are available the inverse problem for a single data set asks us to find an ode or system thereof that admits the interpolated data set as an approximate solution such an inverse problem can be cast within the framework of fixed point equations so that we seek to approximate the data values by a fixed point of an operator related to the odes the collage coding method replaces the minimization of this approximation error by the minimization of the so called collage distance the purpose of this paper is to formulate and explore various methods for dealing with the collection of collage distances corresponding to multiple noisy data sets we present three schemes averaging the parameter estimates obtained by minimizing each of the separate collage distances and two approaches arising from goal programming numerous examples are presented

bv supersolutions to equations of 1 laplace and minimal surface type we propose notions of bv supersolutions to the dirichlet problem for the 1 laplace equation the minimal surface equation and equations of similar type we then establish some related compactness and consistency results our main technical tool is a generalized product of l divergence measure fields and gradient measures of bv functions this product crucially depends on the choice of a representative of the bv function and the proofs of its basic properties involve results on one sided approximation and fine semi continuity in the bv context

dynamics in coupled oscillators with recurrent random forcing a pde approach the current paper is devoted to the study of coupled oscillators with recurrent random forcing special attention is given to the solutions having the same recurrence randomness as that of the forcing recurrent random solutions for short by embedding coupled oscillators into coupled parabolic equations it establishes a general theorem on the existence of recurrent random solutions it also finds conditions under which such solutions are unique when the recurrent forcing is actually quasi periodic or almost periodic recurrent solutions are refereed to as quasi periodic or almost periodic solutions in a weak sense and they are quasi periodic or almost periodic in the classical sense under the uniqueness conditions in addition applications of the general theory to coupled duffing type oscillators and josephson junctions are considered and the results obtained extend several existing ones for quasi periodic duffing oscillators

a unified approach to define fuzzy integrals recently the two most general and well known fuzzy integrals sugeno s integral and choquet s integral were characterized it was also shown how both integrals fitted the same formal model and they only differed in the operators used in this paper we try to analyze whether it is possible to improve those characterization theorems and we also study the possibility of defining other fuzzy integrals following the same model but using other operators in a recent paper campos and bolafios 6 characterized two general and well known fuzzy integrals sugeno s integral 11 and choquet s integral 7 the last one also called monotone expectation 2 4 5 6 the two characterization theorems are based on the same formal model of four properties which only differ in the operators used sum and product for choquet s integral maximum and minimum for sugeno s integral two important questions remained open one involved the characterization theorems of these integrals in an attempt to further refine them the second question was to investigate the possibility of defining other fuzzy integrals using different operators but following the same model in this paper we give answers to those problems section 2 is devoted to describing fuzzy integrals defined on sugeno s fuzzy measures particularly sugeno s and choquet s integrals and their characterizations in section 3 we show how the characterization of choquet s integral can be refined whereas the same cannot be made for sugeno s integral finally other fuzzy integrals fitting our formal model are obtained in section 4

fuzzy integrals and conditional fuzzy measures we introduce a fuzzy integral for fuzzy events with respect to l additive fuzzy measures this integral is the canonical generalization of the lehesgue integral a radon nikodym like theorem is used to give the definition of the conditional fuzziness

fractal feature analysis and classification in medical imaging following b b mandelbrot s fractal theory 1982 it was found that the fractal dimension could be obtained in medical images by the concept of fractional brownian motion an estimation concept for determination of the fractal dimension based upon the concept of fractional brownian motion is discussed two applications are found 1 classification 2 edge enhancement and detection for the purpose of classification a normalized fractional brownian motion feature vector is defined from this estimation concept it represented the normalized average absolute intensity difference of pixel pairs on a surface of different scales the feature vector uses relatively few data items to represent the statistical characteristics of the medial image surface and is invariant to linear intensity transformation for edge enhancement and detection application a transformed image is obtained by calculating the fractal dimension of each pixel over the whole medical image the fractal dimension value of each pixel is obtained by calculating the fractal dimension of 7 7 pixel block centered on this pixel

iterative solutions of parameter dependent nonlinear equations of hammerstein type abstract the unique solution of a general nonlinear hammerstein type equation is obtained based on the contraction mapping principle introducing a suitable weighted norm the range of values of the involved parameter allowed by the contraction mapping principle is shown to be increased detailed construction of the suitable weight function is given application to a specific hammerstein integral equation is considered supported by a numerical example

fourier frequencies in affine iterated function systems abstract we examine two questions regarding fourier frequencies for a class of iterated function systems ifs these are iteration limits arising from a fixed finite families of affine and contractive mappings in r d and the ifs refers to such a finite system of transformations or functions the iteration limits are pairs x where x is a compact subset of r d the support of and the measure is a probability measure determined uniquely by the initial ifs mappings and a certain strong invariance axiom the two questions we study are 1 existence of an orthogonal fourier basis in the hilbert space l 2 x and 2 explicit constructions of fourier bases from the given data defining the ifs

random fixed points of 1 set contractive random maps in frechet spaces a random fixed point theorem for more general 1 set contractive random operators in frechet spaces is proved as applications some random fixed point theorems for nonexpansive semicontractive and lane random operators are also derived thus the results of itoh j math anal appl 67 1979 261 273 lin proc amer math soc 123 1995 1167 1176 proc amer math soc 103 1988 1129 1135 shahzad j math anal appl 203 1996 712 718 tan and yuan stochastic anal appl 15 1997 103 123 and xu proc amer math soc 110 1990 495 500 are extended

fixed point theorems for random pseudo contractive mappings abstract very recently in fierro et al 2009 6 we obtained a general principle to prove the existence of random fixed point theorems as a consequence of this we have been able to obtain various generalizations for pseudo contractive mappings with rather simple proofs in addition while we were deriving these extensions for random operators some deterministic results arose which also appear to be new

the collage coding method and its application to an inverse problem for the lorenz system abstract a lorenz system inverse problem featuring noisy partial data sets is considered via the method of collage coding collage coding is a rigorously established approach to such problems with its roots in fractal imaging and its theoretical basis being banach s fixed point theorem and some recent related results for comparison purposes results for this inverse problem obtained by using other methods are mentioned a framework for treating general inverse problems involving partial data sets in a similar way is also outlined

a note on λ additive fuzzy measures abstract a relation between additive fuzzy measures and measures is given this relation is used to prove some properties of additive fuzzy measures

random sets as imprecise random variables given a random set coming from the imprecise observation of a random variable we study how to model the information about the probability distribution of this random variable specifically we investigate whether the information given by the upper and lower probabilities induced by the random set is equivalent to the one given by the class of the probabilities induced by the measurable selections together with sufficient conditions for this we also give examples showing that they are not equivalent in all cases

characterization and comparison of sugeno and choquet integrals abstract starting from the concept of equiordered functions we characterize two types of fuzzy integrals that can be defined on any kind of fuzzy measure sugeno and choquet integrals the characterization theorems that we obtain allow us to carry out a comparative study of these two fuzzy integrals pointing out their formal similarities and their conceptual differences

applications of the proximity map to random fixed point theorems in hilbert spaces a random approximation theorem for 1 set contractive random operators is proved as applications some random fixed point theorems are derived

a generalized fractal transform for measure valued images abstract fractal image coding generally seeks to express an image as a union of spatially contracted and greyscale modified copies of subsets of itself generally images are represented as functions u x and the fractal coding method is conducted in the framework of 2 or in this paper we formulate a method of fractal image coding on measure valued images at each point x x is a probability measure over the range of allowed greyscale values we construct a complete metric space y d y of measure valued images x m r g where x is the base or pixel space and m r g is the set of probability measures supported on the greyscale range r g a generalized fractal transform m is formulated over the metric space y d y under suitable conditions m y y is contractive implying the existence of a unique fixed point measure valued function m

new fixed points results for 1 set contractive set valued maps abstract new fixed point theorems and random fixed point theorems are presented for multivalued maps

review measures of divergence on credal sets when there is uncertainty about the values of a variable it is possible to have different pieces of information about it this can be due to the fact that they represent the points of view of different agents and these agents have followed different criteria when codify the pieces of information by means of numbers the aim of this paper is to provide tools for the comparison of these representations this is done in the framework of imprecise probabilities more concretely the credal set theory is used the reason is that credal sets are very general including as particular cases possibility theory probability theory and belief functions so it can serve as basis to compare the representations of information obtained by following these formalisms the measures used for comparison are inconsistency measure inclusion index and informative distance

restored fuzzy measures in expert decision making the paper deals with problems of fuzzy measure restoration from insufficient data on a finite set the proposed approach is constructed in the class of second order choquct capacities fuzzy sets and systems 31 1989 23 reports of the enlarged session of i vekua inst appl math 14 1999 31 ann inst fourier 5 1953 131 when the fuzzy weights of singletons are known this essentially concerns certain frequency distributions where the nature of additivity is doubtful because of the fuzzy nature of data distribution this is the indisputable condition for the introduction of a fuzzy measure but the insufficient one for its construction measures of specificity indices of uncertainty and estimators of approximations are calculated some approximation properties are proved using the approach of a kaufman s experton theory les expertons hermes paris 1987 the unique fuzzy subset fuzzy object is constructed from the associated probabilities fuzzy sets and systems 31 1989 23 of the restored fuzzy measure the application of the constructed method is illustrated by an example of the processing of certain insufficient statistical data of the georgian language as a result it becomes possible to derive estimates for the georgian language on the whole

using the collage method to solve one dimensional two point boundary value problems at steady state abstract we consider an inverse problem for two point boundary value problems bvps d u f x q x u x u a u a u b u b where the goal is to recover an approximation of the physically meaningful functions of x and parameters in the differential operator d we rewrite the bvp inverse problem as an initial value problem ivp inverse problem and recast this inverse problem in terms of approximating a target function by the fixed point of a contractive operator on a complete metric space we formulate different collage coding frameworks to solve such problems although the approach has broad applicability we focus on two model problems approximating the variable diffusivity in a steady state heat flow equation and approximating the flexural rigidity in a steady state vibrational beam we present two examples each treated with three different frameworks

representation of fuzzy measures through probabilities abstract in this paper we develop a method to study fuzzy measures associating certain sets of probabilities to them this development is based on the consideration of one property of a fuzzy integral called monotone expectation some results about the monotone expectation in relation to associated probabilities are also obtained

random fixed point theorems and approximation in cones a very general random fixed point theorem is first proved as applications some random approximation theorems and random fixed point theorems are obtained recent results due to itoh j math anal appl 67 1979 261 273 lin proc amer math soc 103 1988 502 506 and xu proc amer math soc 110 1990 495 500 either are improved or are direct consequences of our results the stochastic versions of the recent results of lin 1988 and li proc amer math soc 97 1986 277 280 are also given

network of probabilities associated with a capacity of order 2 abstract this paper studies capacities of order 2 from a geometric point of view that is from convex polytope of probabilities defined by them this convex polytope is characterized by means of a network of probabilities representing relationships among vertices defined by the edges interesting properties may be obtained about the capacities from this network

extensions of fuzzy aggregation abstract we discuss the equivalence between aggregation of fuzzy sets and integration with respect to a special class of non additive set functions both fuzzy integral and choquet integral are considered first we study aggregation of a finite family of fuzzy sets and then we extend our results to aggregation of an infinite family the concepts of comonotonic maxitivity and additivity play a central role we argue that for the purpose of aggregating fuzzy sets comonotonic maxitivity is a more desirable requirement than comonotonic additivity in the absence of any such requirement we explore a wider class of aggregation procedures another important subject that we study is a comparison between two aggregation functions and we obtain a simple characterization in both the finite and infinite case our results are related to concepts that were studied in the three areas where non additive set functions and integrals were found particularly useful fuzzy sets theory mathematical economics and mathematical statistics

power domains and iterated function systems we introduce the notion of weakly hyperbolic iterated function system ifs on a compact metric space which generalises that of hyperbolic ifs based on a domain theoretic model which uses the plotkin power domain and the probabilistic power domain respectively we prove the existence and uniqueness of the attractor of a weakly hyperbolic ifs and the invariant measure of a weakly hyperbolic ifs with probabilities extending the classic results of hutchinson for hyperbolic ifss in this more general setting we also present finite algorithms to obtain discrete and digitised approximations to the attractor and the invariant measure extending the corresponding algorithms for hyperbolic ifss we then prove the existence and uniqueness of the invariant distribution of a weakly hyperbolic recurrent ifs and obtain an algorithm to generate the invariant distribution on the digitised screen the generalised riemann integral is used to provide a formula for the expected value of almost everywhere continuous functions with respect to this distribution for hyperbolic recurrent ifss and lipschitz maps one can estimate the integral up to any threshold of accuracy

inverse problems for random differential equations using the collage method for random contraction mappings in this paper we are concerned with differential equations with random coefficients which will be considered as random fixed point equations of the form t w x w x w w w here t wxx x is a random integral operator w f p is a probability space and x is a complete metric space we consider the following inverse problem for such equations given a set of realizations of the fixed point of t possibly the interpolations of different observational data sets determine the operator t or the mean value of its random components as appropriate we solve the inverse problem for this class of equations by using the collage theorem for contraction mappings

solution of an inverse problem for fractals and other sets abstract the problem of providing succinct approximate descriptions of given bounded subsets of rn can be solved by application of the contraction mapping principle