caristi s fixed point theorem and selections of set valued contractions we show without the axiom of choice that the zermelo theorem implies directly a restriction of the caristi fixed point theorem to continuous functions under the axiom of choice this restriction is proved to be equivalent to caristi s theorem we also discuss kirk s problem on an extension of the caristi theorem and we establish two selection theorems for set valued contractions

fixed points of mizoguchi takahashi contraction on a metric space with a graph and applications abstract in this paper we extend mizoguchi takahashi s fixed point theorem for multi valued mappings on a metric space endowed with a graph as an application we establish a fixed point theorem on an e chainable metric space for mappings satisfying mizoguchi takahashi contractive condition uniformly locally also we establish a result on the convergence of successive approximations for certain operators not necessarily linear on a banach space as another application consequently this result yields the kelisky rivlin theorem on iterates of the bernstein operators on the space c 0 1 and also enables us study the asymptotic behaviour of iterates of some nonlinear bernstein type operators on c 0 1

controllability for systems governed by semilinear differential inclusions in a banach space with a noncompact semigroup abstract we study the controllability problem for a system governed by a semilinear differential inclusion in a banach space not assuming that the semigroup generated by the linear part of inclusion is compact instead we suppose that the multivalued nonlinearity satisfies the regularity condition expressed in terms of the hausdorff measure of noncompactness it allows us to apply the topological degree theory for condensing operators and to obtain the controllability results for both upper caratheodory and almost lower semicontinuous types of nonlinearity as application we consider the controllability for a system governed by a perturbed wave equation

coupled fixed point theorems for multi valued nonlinear contraction mappings in partially ordered metric spaces abstract in this paper we establish two coupled fixed point theorems for multi valued nonlinear contraction mappings in partially ordered metric spaces the theorems presented extend some results due to ciric 2009 3 an example is given to illustrate the usability of our results

mizoguchi takahashi s fixed point theorem is a real generalization of nadler s abstract we give an example which says that mizoguchi takahashi s fixed point theorem for set valued mappings is a real generalization of nadler s we also give a very simple proof of mizoguchi takahashi s theorem

corrigendum to coincidence and fixed points for multi valued mappings and its application to nonconvex integral inclusions j comput appl math 283 2015 201 217 abstract in a recent paper h k pathak r p agarwal y j cho coincidence and fixed points for multi valued mappings and its application to nonconvex integral inclusions j comput appl math 283 2015 201 217 the authors have studied some problems on coincidence points and fixed points of multi valued mappings in order to illustrate the generality of their main result theorem 3 2 with respect to older related results nadler s berinde berinde mizoguchi takahashi and du s fixed point theorem the authors presented two examples i e examples 3 3 and 3 4 the main aim of this note is to show that example 3 3 fails in proving the generality of theorem 3 2 over berinde berinde s fixed point theorem

state reduction information and entropy in quantum measurement processes information obtained by a quantum measurement process performed on a physical system and the entropy change of the measured physical system are considered in detail it is shown that the condition for the amount of information obtained by the quantum measurement process to be represented by the shannon mutual entropy is that the intrinsic observable of the measured physical system commutes with the operational observable defined by the quantum measurement process when some measurement outcome is obtained the decrease of the shannon entropy of the measured system is compared with that of the von neumann entropy furthermore a condition is established under which the amount of information that can be established by the quantum measurement process becomes equal to the decrease of the shannon entropy of the measured physical system

topological structure of solution sets to asymptotic boundary value problems abstract topological structure is investigated for second order vector asymptotic boundary value problems because of indicated obstructions the r structure is firstly studied for problems on compact intervals and then by means of the inverse limit method on non compact intervals the information about the structure is furthermore employed by virtue of a fixed point index technique in frechet spaces developed by ourselves earlier for obtaining an existence result for nonlinear asymptotic problems some illustrating examples are supplied

ekeland s variational principle and its equivalent theorems in vector optimization we present a simple proof of vectorial ekeland s variational principle vectorial caristi s fixed point theorem and vectorial takahashi s nonconvex minimization theorem equivalences between the three theorems are also given

nonlinear error bounds for lower semicontinuous functions on metric spaces as a development of the theory of linear error bounds for lower semicontinuous functions defined on complete metric spaces introduced in aze et al nonlinear anal 49 643 670 2002 and refined in aze and corvellec esaim control optim calc var 10 409 425 2004 we propose a similar approach to nonlinear error bounds based on the notion of strong slope the variational principle and the change of metric principle the latter allowing to obtain sharp estimates for such error bounds through a reduction to the linear case

multivalued f weakly picard mappings recently m berinde and v berinde m berinde v berinde on a general class of multi valued weakly picard mappings j math anal appl in press extended the notion of weak contraction from single valued mappings to multivalued mappings and obtained some convergence theorems for the picard iteration associated with multivalued weak contractions we further extended the notion of weak contraction and introduced the notions of multivalued f weak contraction and generalized multivalued f weak contraction we obtain some coincidence and fixed point theorems our results extend m berinde v berinde on a general class of multi valued weakly picard mappings j math anal appl in press and those contained therein

impulsive mild solutions for semilinear differential inclusions with nonlocal conditions in banach spaces abstract in this paper we deal with the existence of impulsive mild solutions for semilinear differential inclusions with nonlocal conditions where the linear part generates an evolution system and the nonlinearity satisfies the lower scorza dragoni property our theorems extend the existence propositions proved by fan in 2010 an example is presented

fixed point theorems for set valued contractions in complete metric spaces abstract the fixed point theory of set valued contractions which was initiated by nadler s b nadler jr multi valued contraction mappings pacific j math 30 1969 475 488 was developed in different directions by many authors in particular by s reich fixed points of contractive functions boll unione mat ital 5 1972 26 42 n mizoguchi w takahashi fixed point theorems for multivalued mappings on complete metric spaces j math anal appl 141 1989 177 188 y feng s liu fixed point theorems for multi valued contractive mappings and multi valued caristi type mappings j math anal appl 317 2006 103 112 in the present paper the concept of contraction for set valued maps in metric spaces is introduced and the conditions guaranteeing the existence of a fixed point for such a contraction are established one of our results essentially generalizes the nadler and feng liu theorems and is different from the mizoguchi takahashi result the second result is different from the reich and mizoguchi takahashi results the method used in the proofs of our results is inspired by mizoguchi takahashi and feng liu s ideas comparisons and examples are given

local completeness drop theorem and ekeland s variational principle by using a very general drop theorem in locally convex spaces we obtain some extended versions of ekeland s variational principle which only need assume local completeness of some related sets and improve hamel s recent results from this we derive some new versions of caristi s fixed points theorems in the framework of locally convex spaces we prove that danes drop theorem ekeland s variational principle caristi s fixed points theorem and phelps lemma are equivalent to each other

common fixed point properties for a family of set valued mappings abstract in this paper we study common fixed point properties for a family of mappings we present the extensions of caristi s fixed point theorem and markov kakutani fixed point theorem for a family of set valued mappings

some new results and generalizations in metric fixed point theory abstract the main purpose of this paper is the study of the generalization of some results given in m berinde v berinde on a general class of multi valued weakly picard mappings j math anal appl 326 2007 772 782 and references therein some generalizations of the mizoguchi takahashi fixed point theorem kannan s fixed point theorems and chatterjea s fixed point theorems are established by using our new fixed point theorems

some new fixed point theorems of generalized nonlinear contractive multivalued maps in complete metric spaces in this paper we present some new fixed point theorems for generalized nonlinear contractive multivalued maps and these results generalize or improve the corresponding recent fixed point results in the literature

fixed point theorems for generalized metrically inward maps we prove fixed point results for multimaps satisfying a generalized metric or an metric inwardness condition our results extend generalize or improve several known results

some equivalent formulations of the generalized ekeland s variational principle and their applications abstract in this paper we first give a generalized takahashi s existence theorem from the existence theorem we establish some equivalence relations between generalized caristi s fixed point theorems and generalized ekeland s variational principles some applications to the existence theorems of weak sharp minima and global error bounds for lower semicontinuous functions are also given

common fixed point theorems and variational principle in generating spaces of quasi metric family in this paper we introduce the concept of order relation in generating spaces of quasi metric family and establish common fixed point theorems for set valued mappings in this spaces as consequences we also give the variational principle fixed point theorems for single valued and set valued mappings and equivalence between them in complete generating spaces of quasi metric family some applications of these results to fuzzy metric spaces in sense of kaleva and seikkala 1984 and probabilistic metric spaces are presented

mapping theorems for gateaux differentiable and accretive operators let p be a nonlinear operator mapping the banach space x into the banach space y there are many approaches to studying solvability of the equation px y for y e y a considerable number of which involve local or infinitesimal assumptions on the operator p this is due in part to the fact that p frequently arises from a differential or integral operator which has monotonicity or smoothness properties for which local apriori estimates are readily obtainable in this paper we derive mapping theorems for operators p satisfying two different kinds of local assumptions differentiability assumptions and monotonicity assumptions our approach in the former case relies on an abstract newton kantorovich scheme which was pioneered by m altman see for example l and further developed in 19 in the latter case we extend some results of f e browder using a combination of both new and standard techniques in each case our basic technique involves an application of a new version of ekeland s theorem which we derive from a fundamental maximal principle of h brezis and f e browder in section 2 of this paper we derive our new version of ekeland s theorem and in section 3 apply this result to nonlinear operators using different and by now standard techniques we prove a domain invariance result in section 4 needed for our result an accretive operators

ekeland s variational principle for vectorial multivalued mappings in a uniform space abstract in this paper we establish ekeland s variational principle and an equilibrium version of ekeland s variational principle for vectorial multivalued mappings in the setting of separated sequentially complete uniform spaces our approaches and results are different from those in chen et al 2008 hamel 2005 and lin and chuang 2010 13 14 15 as applications of our results we study vectorial caristi s fixed point theorems and takahashi s nonconvex minimization theorems for multivalued mappings and their equivalent forms in a separated sequentially complete uniform space we also apply our results to study maximal element theorems which are unified methods of several variational inclusion problems our results contain many known results in the literature fang 1996 21 and will have many applications in nonlinear analysis

existence in the large for nonlinear delay evolution inclusions with nonlocal initial conditions in this paper we provide a sufficient condition for the existence of c0 solutions for a class of nonlinear functional differential evolution equation of the form u t au t f t t r f t f t u t ut t r u t g u t t 0 where x is a real banach space a is the infinitesimal generator of a nonlinear compact semigroup f r x c 0 d a x is a nonempty convex and weakly compact valued multi function and g cb d a c 0 d a

existence of the solution to variational inequality optimization problem and elliptic boundary value problem through revisited best proximity point results abstract in this paper we establish some results regarding the existence of the solution to variational inequality optimization problem and elliptic boundary value problem in hilbert spaces our strategy consists in establishing new best proximity point results in the metric spaces by introducing the concept of cyclic orbital simulative contractions we also provide nontrivial examples to show that our results are proper generalization further we improve the recent best proximity results for mappings satisfying proximal simulative conditions due to abbas et al 2017 samet 2015 and tchier et al 2016 via new class of simulation functions our results unify extend and generalize various existing results

on some nonlinear problems induced by an abstract maximal element principle abstract in this paper by applying an abstract maximal element principle on quasi ordered sets established by lin and du we obtain a generalized brezis browder principle system vectorial versions of ekeland s variational principle and maximal element principle and a vectorial version of takahashi s nonconvex minimization theorem moreover we investigate the equivalence between scalar versions and vectorial versions of these results

ekeland s variational principle minimax theorems and existence of nonconvex equilibria in complete metric spaces abstract in this paper we introduce the concept of function which generalizes the concept of w distance studied in the literature we establish a generalized ekeland s variational principle in the setting of lower semicontinuous from above and functions as applications of our ekeland s variational principle we derive generalized caristi s common fixed point theorems a generalized takahashi s nonconvex minimization theorem a nonconvex minimax theorem a nonconvex equilibrium theorem and a generalized flower petal theorem for lower semicontinuous from above functions or lower semicontinuous functions in the complete metric spaces we also prove that these theorems also imply our ekeland s variational principle

mizoguchi takahashi s type fixed point theorem recently eldred a a eldred j anuradha p veeramani on equivalence of generalized multi valued contactions and nadler s fixed point theorem j math anal appl 2007 doi 10 1016 j jmaa 2007 01 087 claimed that nadler s s b nadler jr multivalued contraction mappings pacific j math 30 1969 475 488 fixed point theorem is equivalent to mizoguchi takahashi s n mizoguchi w takahashi fixed point theorems for multivalued mappings on complete metric space j math anal appl 141 1989 177 188 fixed point theorem very recently suzuki t suzuki mizoguchi takahashi s fixed point theorem is a real generalization of nadler s j math anal appl 2007 doi 10 1016 j jmaa 2007 08 022 produced an example to disprove their claim and showed that mizoguchi takahashi s fixed point theorem is a real generalization of nadler s fixed point theorem we refine generalize mizoguchi takahashi s fixed point theorem our result improves a recent result by klim and wadowski d klim d wardowski fixed point theorems for set valued contractions in complete metric spaces j math anal appl 334 1 2007 132 139 and extends hicks and rhoades t l hicks b e rhoades a banach type fixed point theorem math japonica 24 1979 327 330 fixed point theorem to multivalued maps

a class of nonlinear evolution equations subjected to nonlocal initial conditions abstract we prove the existence of c 0 solutions for a class of nonlinear evolution equations subjected to nonlocal initial conditions of the form u t a u t f t f t f t u t u 0 g u where a d a x x is an m accretive operator acting on the infinite dimensional banach space x f 0 2 d a x is an almost strongly weakly u s c multi function which satisfies an appropriate sign condition while g c 0 2 d a d a is a continuous function

existence results and asymptotic behavior for nonlocal abstract cauchy problems the purpose of this paper is to study the existence and asymptotic behavior of solutions for cauchy problems with nonlocal initial datum generated by accretive operators in banach spaces

multi valued nonlinear contraction mappings abstract two concepts of nonlinear contractions for multi valued mappings in complete metric spaces are introduced and three fixed point theorems are proved presented theorems are generalizations of very recent fixed point theorems due to klim and wardowski d klim d wardowski fixed point theorems for set valued contractions in complete metric spaces j math anal appl 334 2007 132 139 and feng and liu y feng s liu fixed point theorems for multi valued contractive mappings and multi valued caristi type mappings j math anal appl 317 2006 103 112 as well as a fixed point theorem of mizoguchi and takahashi n mizoguchi w takahash fixed point theorems for multi valued mappings on complete metric spaces j math anal appl 141 1989 177 188 and several others an example is given to show that presented results are genuine generalizations our results are also some contribution to an open problem raised by reich s reich fixed points of contractive functions boll unione mat ital 5 1972 26 42 s reich some fixed point problems atti acad naz lincei 57 1974 194 198 s reich some problems and results in fixed point theory contemp math 21 1983 179 187

a generalization of the banach contraction principle one of the most fundamental fixed point theorems is banach s contraction principle of which the following conjecture is a generalization generalized banach contraction conjecture gbcc let t be a self map of a complete metric space x d and let 0 m 1 let j be a positive integer assume that for each pair x y x min d tkx tky 1 k j md x y then t has a fixed point unlike banach s original theorem the case j 1 the above hypothesis does not compel t to be continuous in this paper we use a density argument coupled with ramsey s theorem from combinatorics to establish the gbcc for arbitrary j without the assumption of continuity it is known that the case j 3 includes instances where t is not continuous at any nonisolated point of x the arguments are constructive and may be useful in establishing other fixed point theorems without appealing to the axiom of choice

equivalents to ekeland s variational principle in uniform spaces abstract a minimal element theorem on sequentially complete uniform spaces is presented that generalizes earlier results of pacific j math 55 2 1974 335 341 proc amer math soc 108 3 1990 707 714 two more equivalent formulations of the minimal element theorem are given it is applied to derive new versions of ekeland type theorems which improve results of j math anal appl 202 1996 398 412 finally the minimal element theorem is used to obtain an ekeland type theorem for functions with values in a linear space without topological structure

fixed point results for set valued contractions by altering distances in complete metric spaces nadler s contraction principle has led to fixed point theory of set valued contraction in non linear analysis inspired by the results of nadler the fixed point theory of set valued contraction has been further developed in different directions by many authors in particular by reich mizoguchi takahashi feng liu and many others in the present paper the concept of generalized contractions for set valued maps in metric spaces is introduced and the existence of fixed point for such a contraction are guaranteed by certain conditions our first result extends and generalizes the nadler feng liu and klim wardowski theorems and the second result is different from the reich and mizoguchi takahashi results as a consequence we derive some results related to fixed point of set valued maps satisfying certain conditions of integral type

on a general class of multi valued weakly picard mappings abstract the concept of weak contraction from the case of single valued mappings is extended to multi valued mappings and then corresponding convergence theorems for the picard iteration associated to a multi valued weak contraction are obtained the main results in this paper extend improve and unify a multitude of classical results in the fixed point theory of single and multi valued contractive mappings and also improve recent results from the paper p z daffer h kaneko fixed points of generalized contractive multi valued mappings j math anal appl 192 1995 655 666

equivalent formulations of ekeland s variational principle abstract we prove that for some 0 inf x f inf x f e there exists y x such that 0

a drop theorem without vector topology abstract danes drop theorem is extended to bornological vector spaces an immediate application is to establish ekeland type variational principle and its equivalence caristi fixed point theorem in bornological vector spaces meanwhile since every locally convex space becomes a convex bornological vector space when equipped with the canonical von neumann bornology qiu s generalization of danes work to locally convex spaces is recovered

fixed point theorems for multi valued contractions in complete metric spaces abstract in this paper the concept of a contraction for multi valued mappings in a metric space is introduced and the existence theorems for fixed points of such contractions in a complete metric space are proved presented results generalize and improve the recent results of y feng s liu y feng s liu fixed point theorems for multi valued contractive mappings and multi valued caristi type mappings j math anal appl 317 2006 103 112 d klim d wardowski d klim d wardowski fixed point theorems for set valued contractions in complete metric spaces j math anal appl 334 2007 132 139 and several others the method used in the proofs of our results is new and is simpler than methods used in the corresponding papers two examples are given to show that our results are genuine generalization of the results of feng and liu and klim and wardowski

ekelandʼs variational principle for an l 0 valued function on a complete random metric space abstract motivated by the recent work on conditional risk measures this paper studies the ekeland s variational principle for a proper lower semicontinuous and lower bounded l 0 valued function where l 0 is the set of equivalence classes of extended real valued random variables on a probability space first we prove a general form of ekeland s variational principle for such a function defined on a complete random metric space then we give a more precise form of ekeland s variational principle for such a local function on a complete random normed module finally as applications we establish the bishop phelps theorem in a complete random normed module under the framework of random conjugate spaces

fixed point theorems for multi valued contractive mappings and multi valued caristi type mappings abstract in this paper the famous banach contraction principle and caristi s fixed point theorem are generalized to the case of multi valued mappings our results are extensions of the well known nadler s fixed point theorem s b nadler jr multi valued contraction mappings pacific j math 30 1969 475 487 as well as of some caristi type theorems for multi valued operators see n mizoguchi w takahashi fixed point theorems for multivalued mappings on complete metric spaces j math anal appl 141 1989 177 188 j p aubin optima and equilibria an introduction to nonlinear analysis grad texts in math springer verlag berlin 1998 p 17 s s zhang q luo set valued caristi fixed point theorem and ekeland s variational principle appl math mech 10 2 1989 111 113 in chinese english translation appl math mech english ed 10 2 1989 119 121 etc

a generalized ekeland vector variational principle and its applications in optimization abstract in this paper we give a generalized ekeland vector variational principle by using the principle we extend and improve the related results in sharp efficiency in the framework of locally convex spaces we introduce two kinds of generalized sharp efficiencies and prove that they are equivalent in particular we show that a sharp efficient solution with respect to an interior point of the ordering cone is also one with respect to every interior point moreover we introduce the generalized takahashi s condition and the generalized hamel s condition for vector valued functions from the generalized ekeland principle we deduce that the two conditions are equivalent from this we discuss the relationship between the distance of f x from e f x and the distance of x from e f where e f x denotes the efficient point set of f x and e f denotes the efficient solution set

a generalization of mizoguchi and takahashi s theorem for single valued mappings in partially ordered metric spaces abstract we present a generalization of mizoguchi and takahashi s fixed point theorem for single valued mappings in partially ordered metric spaces as an application of the main result we give an existence and uniqueness theorem for the solution of a periodic boundary value problem

the first order necessary conditions for nonsmooth variational and control problems the first order necessary conditions for nonsmooth problems of lagrange bolza multiple integral and optimal control are given the necessary conditions are expressed in terms of differential inclusions we deal with some new differentials that generalize the differential of frechet in particular the pontryagin maximum principle is proved without the assumption of continuous differentiability

a near subtraction result in metric spaces the locally closed graph case abstract this paper concerns a near subtraction result for multifunctions with locally closed graph in metric spaces

on maximal element theorems variants of ekeland s variational principle and their applications abstract in this paper we establish several different versions of generalized ekeland s variational principle and maximal element theorem for functions in complete metric spaces the equivalence relations between maximal element theorems generalized ekeland s variational principle generalized caristi s common fixed point theorems and nonconvex maximal element theorems for maps are also proved moreover we obtain some applications to a nonconvex minimax theorem nonconvex vectorial equilibrium theorems and convergence theorems in complete metric spaces

fixed point theorems for generalized contractive multi valued maps in n mizoguchi w takahashi fixed point theorems for multi valued mappings on complete metric spaces j math anal appl 141 1989 177 188 the authors gave a positive answer to the conjecture of s reich concerning the existence of fixed points of multi valued mappings that satisfy certain contractive conditions in this paper we establish some results for multi valued mappings that satisfy a generalized contractive condition in a way that it contains mizoguchi s result as one of its special cases in addition our results not only improve the results of kiran and kamran q kiran t kamran nadler s type principle with high order of convergence nonlinear anal tma 69 2008 4106 4120 and some results of agarwal et al r p agarwal jewgeni dshalalow donal o regan fixed point and homotopy results for generalized contractive maps of reich type appl anal 82 4 2003 329 350 but also provide the high order of convergence of the iterative scheme and error bounds as an application of our results we obtain an existence result for a class of integral inclusions

some results on set valued contractions in abstract metric spaces abstract in this paper the concept of contractive set valued maps in the frame of abstract metric spaces is studied and the existence of fixed points for such maps is guaranteed under certain conditions consequently several known fixed point results are either generalized or extended including the corresponding recent fixed point results of wardowski d wardowski endpoints and fixed points of set valued contractions in cone metric spaces nonlinear anal 71 2009 512 516 as well as klim and wardowski d klim d wardowski dynamic process and fixed points of set valued nonlinear contractions in cone metric spaces nonlinear anal 71 2009 5170 5175 examples are given to show that our results are distinct from the existing ones

stability results for ekeland s e variational principle and cone extremal solutions given x a banach space and f x a a proper lower semicontinuous function which is bounded from below the ekeland s e variational principle asserts the existence of a point xi in x which we call e extremal with respect to f which satisfies fu fxi e u xi for all u x u xi by using set convergence notions kuratowski painleve mosco bounded hausdorff and their epigraphical versions we study the semi continuity properties of the mapping which to f associates e ext f the set of such e extremal points the key for the geometrical understanding of such properties is to consider the equivalent phelps extremization principle which given a closed set d in x and a partial ordering with respect to a pointed cone associates the set of elements of d maximal with respect to this order direct or potential applications are given in various fields multicriteria optimization numerical algorithmic calculus of variations

converses to fixed point theorems of zermelo and caristi let x be an abstract nonempty set and t be a self map of x let per t and fix t denote the sets of all periodic points and all fixed points of t respectively our main theorem says that if pert fixt then there exists a partial ordering such that every chain in x has a supremum and for all x x x tx this result is a converse to zermelo s fixed point theorem we also show that from a purely set theoretical point of view fixed point theorems of zermelo and caristi are equivalent finally we discuss relations between caristi s theorem and its restriction to mappings satisfying caristi s condition with a continuous real function

on equivalence of generalized multi valued contractions and nadler s fixed point theorem we consider two generalizations of nadler s theorem one proved by mizoguchi and takahashi in response to the reich conjecture and another theorem proved by kaneko we show that due to the additional conditions of these theorems the given multi valued map reduces to a multi valued contraction map we prove this result by showing that the orbit of the multi valued map is bounded under the contractive conditions of the two generalizations

fixed point theorems for multivalued mappings on complete metric spaces on obtient une version multivaluee du theoreme de point fixe de caristi qui est equivalent au principe e variationnel du a ekeland on utilise ce resultat pour obtenir un theoreme qui deduit le theoreme de nadler et un theoreme de point fixe commun pour une application a 1 valeur et une application multivaluee

fixed point theorems for multi valued contractions with w distance some fixed point theorems for a few nonlinear multi valued contraction mappings in complete metric spaces with w distance are proved the results presented in this paper generalize the recent results due to ciric 2009 3 feng and liu 2006 4 klim and wardowski 2007 8 latif and abdou 2011 12 and liu et al 2010 14 seven examples are given to explain our results

remarks on caristi s fixed point theorem and kirk s problem abstract without assumptions on the continuity and the subadditivity of by means of caristi s fixed point theorem we investigated the existence of fixed points for a caristi type mapping which partially answered kirk s problem and improved caristi s fixed point theorem jachymski s fixed point theorem and khamsi s fixed point theorem since is not necessarily assumed to be bounded below on x

topological theory of non autonomous parabolic evolution inclusions on a noncompact interval and applications in this paper we consider the topological structure of the solution set of non autonomous parabolic evolution inclusions with time delay defined on non compact intervals the result restricted to compact intervals is then extended to non autonomous parabolic control problems with time delay moreover as the applications of the information about the structure we establish the existence result of global integral solutions for non autonomous cauchy problems subject to nonlocal condition and prove the invariance of a reachability set for non autonomous control problems under single valued nonlinear perturbations finally some illustrating examples are supplied

multivalued generalized nonlinear contractive maps and fixed points abstract we introduce some notions of generalized nonlinear contractive maps and prove some fixed point results for such maps consequently several known fixed point results are either improved or generalized including the corresponding recent fixed point results of ciric l b ciric multivalued nonlinear contraction mappings nonlinear anal 71 2009 2716 2723 klim and wardowski d klim d wardowski fixed point theorems for set valued contractions in complete metric spaces j math anal appl 334 2007 132 139 feng and liu y feng s liu fixed point theorems for multivalued contractive mappings and multivalued caristi type mappings j math anal appl 317 2006 103 112 and mizoguchi and takahashi n mizoguchi w takahashi fixed point theorems for multivalued mappings on complete metric spaces j math anal appl 141 1989 177 188

nonlinear evolution inclusions topological characterizations of solution sets and applications this paper deals with a nonlinear delay differential inclusion of evolution type involving m dissipative operator and source term of multi valued type in a banach space under rather mild conditions the r structure of c0 solution set is studied on compact intervals which is then used to obtain the r property on non compact intervals secondly the result about the structure is furthermore employed to show the existence of c0 solutions for the inclusion mentioned above subject to nonlocal condition defined on right half line no nonexpansive condition on nonlocal function is needed as samples of applications we consider a partial differential inclusion with time delay and then with nonlocal condition at the end of the paper

quantum measuring processes of continuous observables the purpose of this paper is to provide a basis of theory of measurements of continuous observables we generalize von neumann s description of measuring processes of discrete quantum observables in terms of interaction between the measured system and the apparatus to continuous observables and show how every such measuring process determines the state change caused by the measurement we establish a one to one correspondence between completely positive instruments in the sense of davies and lewis and the state changes determined by the measuring processes we also prove that there are no weakly repeatable completely positive instruments of nondiscrete observables in the standard formulation of quantum mechanics so that there are no measuring processes of nondiscrete observables whose state changes satisfy the repeatability hypothesis a proof of the wigner araki yanase theorem on the nonexistence of repeatable measurements of observables not commuting conserved quantities is given in our framework we also discuss the implication of these results for the recent results due to srinivas and due to mercer on measurements of continuous observables

existence of minimizers on drops for a boundedly generated drop a e a property which holds for instance whenever e is bounded where a belongs to a real banach space x and e subset x is a nonempty convex set we show that for every lower semicontinuous function h x longrightarrow mathbb r cup infty that satisfies sup delta 0 inf x in e delta b x h x h a b x being the unitary open ball in x there exists bar x in a e such that h a ge h bar x and bar x is a strict minimizer of h on the drop bar x e

coincidence point theorems in generating spaces of quasi metric family in this paper we establish some new versions of coincidence point theorems for single valued and multi valued mappings in generating spaces of quasi metric family as applications we utilize our main theorems to prove coincidence point theorems and fixed point theorems for single valued and multi valued mappings in fuzzy metric spaces and probabilistic metric spaces

generalized distance and existence theorems in complete metric spaces abstract in this paper we first introduce the concept of distance on a metric space which is a generalized concept of both w distance and tataru s distance we also improve the generalizations of the banach contraction principle caristi s fixed point theorem ekeland s variational principle and the nonconvex minimization theorem according to takahashi further we discuss the relation between w distance and tataru s distance

the drop theorem the petal theorem and ekeland s variational principle on montre que le principe variationnel d ekeland ou plus precisement une forme legerement modifiee est une consequence d un resultat geometrique connu sous le terme de theoreme de la goutte

coincidence theorems for set valued mappings and ekeland s variational principle in fuzzy metric spaces abstract in this paper we establish a coincidence theorem for set valued mappings in fuzzy metric spaces with a view to generalizing downing kirk s fixed point theorem in metric spaces as consequences we obtain caristi s coincidence theorem for set valued mappings and a more general type of ekeland s variational principle in fuzzy metric spaces further we also give a direct simple proof of the equivalence between these two theorems in fuzzy metric spaces some applications of these results to probabilistic metric spaces are presented

the density of extremal points in ekeland s variational principle in this paper we investigate the density of extremal points appeared in ekeland s variational principle by introducing radial intersections of sets we give a very general result on the density of extremal points in the framework of locally convex spaces this solves a problem proposed by g isac in 1997 from the general result we deduce several convenient criterions for judging the density of extremal points which extend and improve a result of f cammaroto and a chinni using the equivalence between ekeland s variational principle and caristi s fixed point theorem we obtain some density results on caristi s fixed points

probabilistically reversible measurements probabilistically reversible quantum measurements are considered from the information theoretical point of view it is found that an upper bound on the probability of a reversing quantum measurement is given by the generalized bhattacharyya overlap of conditional probabilities of the measurement outcomes the relation between the upper bound of the probability and the information obtained by the quantum measurement is also discussed

some new results for multi valued fractional evolution equations given a closed linear operator a in a banach space x and a multi valued function with convex closed values f 0 b c 0 x 2 x we consider the cauchy problem c d t u t au t f t u t t 0 b u t t t 0 where 0 c d t 0 1 represents the regularized caputo fractional derivative of order we concentrate on the case when the semigroup generated by a is noncompact and obtain nonemptyness of the solution set if in particular x is reflexive and f is weakly upper semicontinuous with respect to the second variable furthermore in this situation topological properties of the set of all solutions are considered

some generalizations of ekeland type variational principle with applications to equilibrium problems and fixed point theory abstract in this paper we introduce the concept of a q function defined on a quasi metric space which generalizes the notion of a function and a w distance we establish ekeland type variational principles in the setting of quasi metric spaces with a q function we also present an equilibrium version of the ekeland type variational principle in the setting of quasi metric spaces with a q function we prove some equivalences of our variational principles with caristi kirk type fixed point theorems for multivalued maps the takahashi minimization theorem and some other related results as applications of our results we derive existence results for solutions of equilibrium problems and fixed point theorems for multivalued maps we also extend the nadler s fixed point theorem for multivalued maps to a q function and in the setting of complete quasi metric spaces as a consequence we prove the banach contraction theorem for a q function and in the setting of complete quasi metric spaces the results of this paper extend and generalize many results appearing recently in the literature

suzuki type fixed point theorems for generalized multi valued mappings on a set endowed with two b metrics abstract in this paper we obtained suzuki type fixed point results for a generalized multi valued mapping on a set equipped with two b metrics as a consequence existence and uniqueness of solution of functional equation arising in dynamical programming is also derived

non autonomous evolution inclusions with nonlocal history conditions global integral solutions abstract this paper is concerned with nonlinear nonlocal differential inclusion of evolution type in frechet spaces defined on right half line the underlying feature of the inclusion under consideration is that it is non autonomous we obtain some compactness characterizations of integral solution sets for the inclusion without nonlinear perturbations then making use of these characterizations we derive a new existence result of global integral solutions for the original inclusion no invariance condition on the nonlinearity is involved the results we obtained here extend the semilinear case of the previous related ones such as i i vrabie existence in the large for nonlinear delay evolution inclusions with nonlocal initial conditions j funct anal 262 2012 1363 1391 and are new even for the case of the nonlinearity being a single valued function

existence for nonlinear evolution inclusions with nonlocal retarded initial conditions abstract in this paper we prove a sufficient condition for the global existence of bounded c 0 solutions for a class of nonlinear functional differential evolution equation of the form u t a u t f t t 0 f t f t u t u t 1 u t n t 0 u t g u t t 0 where x is a real banach space a is the infinitesimal generator of a nonlinear compact semigroup f r d a n 1 x is a nonempty convex weakly compact valued and almost strongly weakly u s c multi function and g c b d a c 0 d a is nonexpansive

coincidence and fixed points for multi valued mappings and its application to nonconvex integral inclusions in this paper we consider some problems on coincidence point and fixed point theorems for multi valued mappings applying the characterizations of p functions we establish some new existence theorems for coincidence point and fixed point distinct from nadler s fixed point theorem berinde berinde s fixed point theorem mizoguchi takahashi s fixed point theorem and du s fixed point theorem for nonlinear multi valued contractive mappings in complete metric spaces our results compliment and extend the main results given by some authors in the literature in the sequel we consider a nonconvex integral inclusion and prove the filippov type existence theorem by using an appropriate norm on the space of selection of a multi function and a multi valued contraction for set valued mappings

the strong ekeland variational principle the strong drop theorem and applications on donne une nouvelle demonstration du theoreme de la goutte generalisee en utilisant des formes renforcees du principe variationnel d ekeland et du theoreme de la goutte et donne de nouveaux resultats et de nouvelles demonstrations de resultats connus sur les proprietes generiques des problemes de minimisation convexes et non convexes

ekeland s variational principle in locally convex spaces and the density of extremal points in this paper we prove a general version of ekeland s variational principle in locally convex spaces where perturbations contain subadditive functions of topology generating seminorms and nonincreasing functions of the objective function from this we obtain a number of special versions of ekeland s principle which include all the known extensions of the principle in locally convex spaces moreover we give a general criterion for judging the density of extremal points in the general ekeland s principle which extends and improves the related known results