the denjoy wolff theorem in cn abstract if d is a bounded and strictly convex domain in c n and f d d is holomorphic and fixed point free then there exists d such that the sequence f n of the iterates of f converges in the compact open topology to the constant mapping taking the value

a fuzzy syllogistic reasoning schema for generalized quantifiers in this paper a new approximate syllogistic reasoning schema is described that expands some of the approaches expounded in the literature into two ways i a number of different types of quantifiers logical absolute proportional comparative and exception taken from theory of generalized quantifiers and similarity quantifiers taken from statistics are considered and ii any number of premises can be taken into account within the reasoning process furthermore a systematic reasoning procedure to solve the syllogism is also proposed interpreting it as an equivalent mathematical optimization problem where the premises constitute the constraints of the searching space for the quantifier in the conclusion

ordinary differential operator and some of its applications to certain meromorphically p valent functions by making use of the well known assertions given in miller and mocanu 1978 13 and nunokawa 1993 14 certain theorems concerning p valently meromorphic strongly starlike and strongly convex functions obtained in this investigation are firstly proved and then their certain consequences which will be interesting or important for analytic and geometric function theory are pointed out

the denjoy wolff theorem for condensing holomorphic mappings if b is the open unit ball of a strictly convex banach space x and f b b is holomorphic condensing with respect to and fixed point free then there exists b such that the sequence lcub fn of the iterates of f converges in the compact open topology to the constant map taking the value

a common fixed point theorem for compatible quasi contractive self mappings in metric spaces a common fixed point theorem for weakly commuting quasi contractive self mappings with contracting orbital diameters in metric spaces v berinde a common fixed point theorem for quasi contractive type mappings ann univ sci budapest 46 2003 81 90 is extended to the more general class of compatible quasi contractive self mappings our result does extend and generalize numerous related results in literature

the denjoy wolff theorem in the open unit ball of a strictly convex banach space letxbe a complex strictly convex banach space with an open unit ballb for each compact holomorphic and fixed point free mappingf b bthere exists bsuch that the sequence fn of iterates offconverges locally uniformly onbto the constant map taking the value

fixed point theorems for discontinuous mapping we prove a generalization of brouwer s famous fixed point theorem to discontinuous maps the main result shows that for discontinuous functions on a compact convex domainx one can always find a pointx x such that x f x is less than a certain measure of discontinuity applications to artificial neural nets economic equilibria and analysis are given

some common fixed point theorems for generalized nonlinear contractive mappings sufficient conditions for the existence of a common fixed point for generalized nonlinear contractive mappings are derived as applications some results on the set of best approximation for this class of mappings are also obtained the proved results generalize and extend various known results in the literature

asymptotics of sobolev orthogonal polynomials for hermite 1 1 coherent pairs abstract in this paper we will discuss asymptotic properties of monic polynomials s n x n 0 orthogonal with respect to the sobolev inner product p q s r p x q x d 0 r p x q x d 1 with 0 d 0 e x 2 d x d 1 x 2 a x 2 b e x 2 d x a b r and a b it is well known that 0 1 is a pair of symmetric 1 1 coherent measures this means that there exist sequences a n n n b n n n a n b n for every n n such that the algebraic relation h n x b n 2 h n 2 x q n x a n 2 q n 2 x n 2 is satisfied where q n x n 0 is the sequence of monic orthogonal polynomials associated with 1 and h n x n 0 is the sequence of monic hermite polynomials we will study the relative asymptotics for sobolev scaled polynomials and we will obtain mehler heine type formulas among others

fixed points for non self operators and domain invariance theorems abstract the purpose of this paper is to discuss some basic problems of the fixed point theory for non self single valued and multivalued generalized contractions as consequences new open operator principles and domain invariance theorems are obtained the results complement and extend some known results in the literature

some families of multivalently analytic functions with negative coefficients abstract the authors introduce and study three novel subclasses of analytic and p valent functions with negative coefficients in addition to finding a necessary and sufficient condition for a function to belong to each of these subclasses a number of other potentially useful properties and characteristics of functions in these subclasses are obtained finally several applications involving an integral operator and certain fractional calculus operators are also considered

a remark on discontinuity at fixed point abstract in this note we give one more solution to the open question of the existence of contractive definitions which are strong enough to generate a fixed point but which do not force the mapping to be continuous at the fixed point r kannan 1969 9 b e rhoades 1988 14

invariant approximations and r subweakly commuting maps the existence of invariant approximations for r subweakly commuting mappings is proved our results extend most of the known results to a new class of noncommuting mappings

some results on existence and approximation in metric fixed point theory some extensions and applications of the synthetic approaches to fixed point theorems introduced recently by angrisani and clavelli are discussed

on certain sufficient conditions for close to convexity in this paper we derive certain sufficient conditions for close to convexity of analytic functions by using the techniques of differential subordinations relevant connections of the results presented here with those obtained in earlier works are pointed out

differential subordination and superordination results for cho kwon srivastava operator making use of the concepts of differential subordination and superordination many subordination and superordination results are obtained for analytic functions in the open unit disk using the cho kwon srivastava operator by investigating appropriate classes of admissible functions sandwich type results are also obtained

a formal theory of generalized intermediate syllogisms in this paper we continue developing the formal theory of intermediate quantifiers expressions such as most few almost all a lot of many a great deal of a large part of a small part of the theory is a fuzzy logic formalization of the concept introduced by peterson in his book we will syntactically prove that 105 generalized aristotle s syllogisms introduced in this book are valid in our theory at the same time we will also prove that syllogisms listed there as invalid are invalid also in our theory therefore we believe that our theory provides a reasonable mathematical model of the generalized syllogistics

fuzzy quantifiers defined over fuzzy domains abstract in this paper we introduce a generalization of the concept of fuzzy quantifier called fuzzy quantifiers over fuzzy domains the development of this generalization is motivated by the impossibility to satisfactorily define the important operation of relativization for standard fuzzy quantifiers we provide basic examples of these quantifiers and define and investigate also several semantic properties of them finally we prove a theorem saying among other things that all these two argument fuzzy quantifiers that possess properties of extension and conservativity are relativizations of one argument fuzzy quantifiers of this kind

remarks on a paper by f browder about contraction throughout this note x denotes a complete metric space with distance function d and t is a map from x into itself powers of t are defined by tax x and t lx t t x n 2 0 occasionally we use the notation xk tkx in particular x0 x x1 tx for the sake of brevity the set x tx t x t x is called an orbit starting at x and denoted by o x the set 0 x y is the union of the two orbits starting at x and y 0 x y xk yk k 3 o the diameter diam a of a nonempty subset a of x is the supremum of the numbers d x y where x and y vary in a the letter 4 denotes a contractive gauge function i e a continuous increasing function from r the non negative reals into r which satisfies 4 s 0

remarks on approximate fixed points abstract a mapping f from a topological space x to a metric space m d is said to be r continuous r 0 if for any x x there exists a neighborhood u x of x such that diam f u x r in 1961 victor klee proved that an r continuous self mapping of a compact convex subset of a banach space always has a invariant point for any r recently h x phu extended klee s result to mappings that are almost r continuous in this note we extend phu s result to compact hyperconvex spaces and to geodesically bounded complete r trees we also extend klee s stability result to certain geodesic spaces

banach operator pairs and common fixed points in hyperconvex metric spaces the purpose of this paper is to establish demarr s well known theorem for an arbitrary family of symmetric banach operator pairs in hyperconvex metric spaces without the compactness assumption we also give necessary and sufficient criteria for the existence of a common fixed point of a semigroup of isometric mappings as an application several results on the invariant best approximation are proved

common fixed point and approximation results for h operator pair with applications abstract the existence of common fixed point results for new classes of noncommuting selfmaps satisfying generalized i contraction or i nonexpansive type conditions is established as applications several invariant best approximation results are proved which unify extend and complement the well known results

contractivity of leader type and fixed points in uniform spaces with generalized pseudodistances abstract recently jachymski and jo wik proved that among various classes of contractions which are introduced and studied in the metric fixed point theory the leader contractions are greatest general contractions in this article we want to show how generalized pseudodistances in uniform spaces can be used to obtain new and general results of leader type without complete graph assumptions about maps and without sequentially complete assumptions about spaces which was not done in the previous publications on this subject the definitions results and methods presented here are new for maps in uniform and locally convex spaces and even in metric spaces examples showing a difference between our results and the well known ones are given

the uniqueness of endpoints for set valued dynamical systems of contractions of meir keeler type in uniform spaces abstract in this paper the concept of the set valued dynamical systems of contractions of meir keeler type in uniform spaces is introduced and conditions guaranteeing the existence and uniqueness of endpoints of these contractions and the convergence to these endpoints of all generalized sequences of iterations of these contractions are established the definition and the result presented here are new for set valued dynamical systems in uniform locally convex and metric spaces and even for single valued maps examples show a fundamental difference between our result and the well known ones

banach operator pairs common fixed points invariant approximations and nonexpansive multimaps abstract common fixed point results are proved for i nonexpansive maps ciric type maps and nonexpansive multimaps invariant approximation results are obtained for these types of maps as applications our results extend or generalize several known results including the recent results of chen and li j chen z li common fixed points for banach operators pairs in best approximation j math anal appl 336 2007 1466 1475 in particular we show that the results of chen and li on banach operator pairs are particular cases of the results of al thagafi and shahzad m a al thagafi n shahzad noncommuting selfmaps and invariant approximations nonlinear anal 64 2006 2778 2786

common fixed points for banach operator pairs in best approximation the notion of banach operator pairs is introduced as a new class of noncommuting maps some common fixed point theorems for banach operator pairs and the existence of the common fixed points of best approximation are presented these results are proved without the assumption of linearity or affinity for either f or g which shows that the concept about banach operator pairs is potentially useful in the study of common fixed points

some subclasses of multivalent functions involving a certain linear operator the authors investigate various inclusion and other properties of several subclasses of the class ap of normalized p valent analytic functions in the open unit disk which are defined here by means of a certain linear operator problems involving generalized neighborhoods of analytic functions in the class ap are investigated finally some applications of fractional calculus operators are considered

common fixed points in best approximation for banach operator pairs with ciric type i contractions abstract the common fixed point theorems similar to those of ciric lj b ciric on a common fixed point theorem of a gregus type publ inst math beograd n s 49 1991 174 178 lj b ciric on diviccaro fisher and sessa open questions arch math brno 29 1993 145 152 lj b ciric on a generalization of gregus fixed point theorem czechoslovak math j 50 2000 449 458 fisher and sessa b fisher s sessa on a fixed point theorem of gregus internat j math math sci 9 1986 23 28 jungck g jungck on a fixed point theorem of fisher and sessa internat j math math sci 13 1990 497 500 and mukherjee and verma r n mukherjee v verma a note on fixed point theorem of gregus math japon 33 1988 745 749 are proved for a banach operator pair as applications common fixed point and approximation results for banach operator pair satisfying ciric type contractive conditions are obtained without the assumption of linearity or affinity of either t or i our results unify and generalize various known results to a more general class of noncommuting mappings

asymptotics of sobolev orthogonal polynomials for hermite coherent pairs abstract let qn be the polynomials orthogonal with respect to the sobolev inner product f g s fg d 0 f g d 1 being 0 1 a coherent pair where one of the measures is the hermite measure the outer relative asymptotics for qn with respect to hermite polynomials are found on the other hand we consider the sobolev scaled polynomials and we obtain the plancherel rotach asymptotics for those as well as a consequence about their zeros

convergence of iterates of nonexpansive mappings and orbits of nonexpansive semigroups abstract let x be a uniformly convex banach space and let c be a bounded closed and convex subset of x assume that c has nonempty interior and is locally uniformly rotund let t be a nonexpansive self mapping of c if t has no fixed point in the interior of c then there exists a unique point x on the boundary of c such that each sequence of iterates of t converges in norm to x we also establish an analogous result for nonexpansive semigroups

fuzzy quantification a state of the art abstract quantified sentences are a very powerful notion for modelling statements in natural language nl but in practice they have been used to solve several problems this paper is intended to offer a global view of the development on this branch until now focusing in the different approaches dealing with quantification specially those involving imprecision called fuzzy quantification we put attention to the different mechanisms for defining them the evaluation methods for measuring their fulfilment as well as the properties they should satisfy

score estimating equations from embedded likelihood functions under accelerated failure time model the semiparametric accelerated failure time aft model is one of the most popular models for analyzing time to event outcomes one appealing feature of the aft model is that the observed failure time data can be transformed to identically independent distributed random variables without covariate effects we describe a class of estimating equations based on the score functions for the transformed data which are derived from the full likelihood function under commonly used semiparametric models such as the proportional hazards or proportional odds model the methods of estimating regression parameters under the aft model can be applied to traditional right censored survival data as well as more complex time to event data subject to length biased sampling we establish the asymptotic properties and evaluate the small sample performance of the proposed estimators we illustrate the proposed methods through applications in two examples

certain subclasses of p valent starlike functions defined by using a differential operator abstract the object of this paper is to introduce two interesting subclasses t n p q and c n p q of p valent starlike functions defined by using a differential operator we obtain coefficient estimates and distortion theorems for functions belonging to these classes the radii of convexity for functions belonging to these classes are also determined finally several applications involving an integral operator and certain fractional calculus operator are also considered

approximation of common fixed points of weakly compatible pairs using the jungck iteration abstract we show that the jungck iteration scheme can be used to approximate the common fixed points of some weakly compatible pairs of generalized quasicontractive operators defined on metric spaces the existence of coincidence points are also discussed for those pair of maps the results are generalizations of well known results of the convergence of picard iterations for single self maps of banach spaces in particular the results improve generalize and extend the recent results of berinde v berinde a common fixed point theorem for compatible quasi contractive self mappings in metric spaces applied mathematics and computation 213 2009 348 354 and answers the open question posed in the paper

certain properties of the dziok srivastava operator the main object of the present paper is to investigate several interesting properties and characteristics of a linear operator h p q s a 1 which was recently introduced and studied in a series of papers by dziok and srivastava appl math comput 103 1999 1 13 adv stud contemp math 5 2002 115 125 integral transform spec funct 14 2003 7 18 the various properties and characteristics of the linear operator h p q s a 1 which are considered in this paper are associated with for example the principle of differential subordination between analytic functions and a certain one parameter family of integral operators

on a result of w a kirk and l m saliga we prove that the conclusion of a result of kirk and saliga j comput appl math 113 2000 141 theorem 4 3 p 149 remain valid for a wide class of contractive gauge functions

best simultaneous approximations asymptotically nonexpansive mappings and variational inequalities in banach spaces abstract the existence of common fixed points is established for three mappings where t is either generalized f g nonexpansive or asymptotically f g nonexpansive on a nonempty subset of a banach space as applications the invariant best simultaneous approximation results are proved and the existence of solution of variational inequalities is obtained our results unify and substantially improve several recent results existing in the current literature

smallest zeros of some types of orthogonal polynomials asymptotics we establish mehler heine type formulas for orthogonal polynomials related to rational modifications of hermite weight on the real line and for hermite sobolev orthogonal polynomials these formulas give us the asymptotic behaviour of the smallest zeros of the corresponding orthogonal polynomials furthermore we solve a conjecture posed in a previous paper about the asymptotics of the smallest zeros of the hermite sobolev polynomials as well as an open problem concerning the asymptotics of these sobolev orthogonal polynomials

neighborhoods of a certain family of multivalent functions with negative coefficients abstract by making use of the familiar concept of neighborhoods of analytic and p valent functions the authors prove coefficient bounds and distortion inequalities and associated inclusion relations for the n neighborhoods of a family of multivalent functions with negative coefficients which is defined by means of a certain nonhomogeneous cauchy euler differential equation relevant connections of the various function classes investigated in this paper with those considered by earlier workers on the subject are also mentioned

on the relation between fuzzy and generalized quantifiers fuzzy quantified sentences have been widely applied for modeling statements in natural language since they allow to represent a broad type of intrinsically imprecise quantified statements that are usually linguistically expressed two different frameworks arise in order to model this imprecision in quantification zadeh s fuzzy quantifiers and the fuzzification of generalized quantification for both models several approaches have been developed for assessing the degree of satisfiability of fuzzy quantified sentences we present and compare both models concluding that although the concept of quantifier in each model has not the same semantics we can establish a connection between them and between the evaluation methods in both theories

some common fixed point theorems for banach operator pairs with applications in best approximation abstract the ordered pair t i of two self maps of a metric space x d is called a banach operator pair if the set f i of fixed points of i is t invariant i e t f i f i some common fixed point theorems for a banach operator pair and the existence of common fixed points of best approximation are presented in this paper the results prove generalize and extend some results of al thagafi m a al thagafi common fixed points and best approximation j approx theory 85 1996 318 323 carbone a carbone applications of fixed point theorems jnanabha 19 1989 149 155 chen and li j chen z li common fixed points for banach operator pairs in best approximations j math anal appl 336 2007 1466 1475 habiniak l habiniak fixed point theorems and invariant approximation j approx theory 56 1989 241 244 jungck and sessa g jungck s sessa fixed point theorems in best approximation theory math japon 42 1995 249 252 sahab khan and sessa s a sahab m s khan s sessa a result in best approximation theory j approx theory 55 1988 349 351 shahzad n shahzad invariant approximations and r subweakly commuting maps j math anal appl 257 2001 39 45 and of few others

fractional calculus and certain starlike functions with negative coefficients abstract a certain subclass t n p of starlike functions in the unit disk is introduced the object of the present paper is to derive several interesting properties of functions belonging to the class t n p various distortion inequalities for fractional calculus of functions in the class t n p are also given

some families of linear operators associated with certain subclasses of multivalent functions making use of a certain linear operator which is defined here by means of the hadamard product or convolution we introduce two novel subclasses p a c a b p l andp a c a b p l of the class a p of normalized p valent analytic functions in the open unit disk the main objective of the present paper is to investigate the various important properties and characteristics of each of these subclasses furthermore several properties involving neighborhoods of functions in these subclasses are investigated we also derive many results for the modified hadamard products of functions belonging to the class p a c a b p l finally some applications of fractional calculus operators are considered

univalent solutions of briot bouquet differential equations let and be complex numbers and let h z be regular in the unit disc u in this article the authors study the briot bouquet differential equation q z frac zq z beta q z gamma h z sufficient conditions are obtained for both the regularity and univalency of the solution in u in addition applications of these results to differential subordinations integral operators and univalent functions are given

classes of multivalent analytic functions involving the dziok srivastava operator the object of the present paper is to investigate some inclusion relationships and a number of other useful properties of several subclasses of multivalent analytic functions which are defined here by using the dziok srivastava operator relevant connections of the results presented here with those obtained in earlier works are pointed out

a certain fractional derivative operator and its applications to a new class of analytic and multivalent functions with negative coefficients recently the authors made use of a certain operator of fractional derivatives in order to introduce and initiate a systematic study of a novel subclass tp of analytic and p valent functions with negative coefficients in this sequel to the aforementioned work they prove a number of closure and inclusion theorems and determine the radii of p valently close to convexity starlikeness and convexity for the class tp they also obtain a class preserving integral operator of the form f z j p z pz z0t 1 t dt p for the class studied here

common fixed points for banach operator pairs with applications the existence of common fixed point results for a banach operator pair under certain generalized contractions is established the invariant best approximation results are proved as applications and the existence of solutions of variational inequalities is obtained we also study the solution of functional equations arising from dynamic programming 2007 elsevier ltd all rights reserved

classes of multivalent functions associated with a convolution operator we investigate several properties of the linear aouf silverman srivastava operator and associated classes of multivalent analytic functions which were introduced and studied by aouf et al m k aouf h silverman h m srivastava some families of linear operators associated with certain subclasses of multivalent functions comp math appl 55 2008 535 549 several theorems are extensions of earlier results of the above paper

banach operator pair and common fixed points for nonexpansive maps abstract let x be a normed space and t and i be two nonexpansive self maps on the closed convex subset c x it is proved that if i t is a banach operator pair and t c is compact then f i t 0 a family of nonexpansive maps is also investigated the well known de marr s fixed point theorem is extended to the noncommuting case by introducing a notion of banach operator family as an application of the theorem the problem for the common fixed point in invariant approximation for convex set is solved directly in a quite different way from the others before

an overview of fuzzy quantifiers i interpretations quantification is an important topic in fuzzy theory and its applications an overview is presented for quantification in fuzzy theory after a brief review of quantifiers in first order logic two approaches of generalizing quantifiers are given the algebraic method and the substitution method by distinguishing the fuzziness of predicates and quantifiers various approaches to quantification in fuzzy logic can be organized quantifiers in first order logic can be generalized in crisp sense and these generalized quantifiers can also be applied to fuzzy sets moreover quantifiers themselves can be fuzzy i e they can only be represented by a fuzzy set these different kinds of quantifications are identified quantifiers relate close to the concept of the cardinality of a fuzzy set which is summarized before investigating fuzzy quantifications different to classical logic various semantics of propositions in fuzzy logic fall into different frameworks which are known as the possibility distribution based reasoning system and the many valued fuzzy logics accordingly numerical and possibilistic interpretation explored in literature are reviewed conforming to these two frameworks

an overview of fuzzy quantifiers ii reasoning and applications abstract in the second part of the overview reasoning with fuzzily defined quantifiers and applications are presented possibility based reasoning is summarized in detail the widely used quantifier extension principle and various reasoning schemas derived from it are discussed some disadvantages of the quantifier extension principle are pointed out although intervalvalued quantifiers are only a special case of general quantifiers some specific properties and results arise from them furthermore they suggest another approach to interence with fuzzy quantifiers reasoning with quantification and several kinds of qualification is introduced this kind of reasoning requires a seamless synthesis of probability theory possibility theory fuzzy logic and belief theory at last the applications of fuzzily defined quantifiers in decision making and fuzzy database systems are introduced

a mehler heine type formula for hermite sobolev orthogonal polynomials we consider a sobolev inner product such as f g s f x g x d 0 x f x g x d 1 x 0 1 with 0 1 being a symmetrically coherent pair of measures with unbounded support denote by qn the orthogonal polynomials with respect to 1 and they are so called hermite sobolev orthogonal polynomials we give a mehler heine type formula for qn when 1 is the measure corresponding to hermite weight on r that is d 1 e x2 dx and as a consequence an asymptotic property of both the zeros and critical points of qn is obtained illustrated by numerical examples some remarks and numerical experiments are carried out for d 0 e x2 dx an upper bound for qn on r is also provided in both cases

on the analysis of set based fuzzy quantified reasoning using classical syllogistics syllogism is a type of deductive reasoning involving quantified statements the syllogistic reasoning scheme in the classical aristotelian framework involves three crisp term sets and four linguistic quantifiers for which the main support is the linguistic properties of the quantifiers a number of fuzzy approaches for defining an approximate syllogism have been proposed for which the main support is cardinality calculus in this paper we analyze fuzzy syllogistic models previously described by zadeh and dubois et al and compare their behavior with that of the classical aristotelian framework to check which of the 24 classical valid syllogistic reasoning patterns or moods are particular crisp cases of these fuzzy approaches this allows us to assess to what extent these approaches can be considered as either plausible extensions of the classical crisp syllogism or a basis for a general approach to the problem of approximate syllogism

common fixed points for p operator pair with applications the existence of common fixed point results for new classes of noncommuting selfmaps satisfying generalized i contraction or i nonexpansive type conditions is established as applications several invariant best approximation results are proved which unify extend and complement the well known results

the structure of generalized intermediate syllogisms abstract in this paper we continue development of the formal theory of intermediate quantifiers which are expressions of the natural language most many few etc in the previous paper we demonstrated that 105 generalized syllogisms are valid in our theory we introduce the generalization of all the figures and we show that for the proof of validity of all the generalized syllogisms we need to prove the validity of only few of them so that the validity of the other ones immediately follows

on kirk s asymptotic contractions abstract recently kirk introduced the notion of asymptotic contractions on a metric space and using ultrapower techniques he obtained an asymptotic version of the boyd wong fixed point theorem in this paper we extend this result and moreover we give a constructive proof of it furthermore we obtain a complete characterization of asymptotic contractions on a compact metric space as a by product we establish a separation theorem for upper semicontinuous functions satisfying some limit condition

applications of multivalent prestarlike functions in the paper we introduce general classes of multivalent analytic functions defined by the subordination in particular we define the class of multivalent prestarlike functions by using the ruscheweyh s duality theory we investigate convolution properties related to multivalent prestarlike functions and various inclusion relationships between defined classes of functions some applications involving well known classes of functions defined by linear operators are also considered