Random common fixed point theorems of set-valued mappings

In this paper, we prove several random common fixed point theorems to general setvalued contractive mappings. These theorems improve and generalize the corresponding results in [1–18].     

Nonempty intersection theorems and system of generalized vector equilibrium problems in product G-convex spaces

By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.     

MAXIMAL ELEMENTS FOR GB-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅰ)

A new family of set-valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set-valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature. Contributed by DING Xie-ping Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan Province of China ([2000]25) Biography: DING Xie-ping (1938∼)     

Some coincidence theorems of set-valued mappings

Browder^[1] obtained the sharpened forms of the Schauder fixed point theorem. Many authors generalized Browder’s results in several aspects. Recently, H.M. Ko and K.K. Tan^[2,3] generalized Browder’s theorems to the coincidence theorems of set-valued mappings. In this paper, we also show some coincidence theorems oj set-valued mappings. They improve and generalize the important results in [1,2,3].     

The best approximation and coincidence theorems for composites of acyclic mappings

ＩｎｔｒｏｄｕｃｔｉｏｎＲｅｃｅｎｔｌｙｔｈｅｒｅｈａｖｅａｐｐｅａｒｅｄａｎｕｍｂｅｒｏｆｎｅｗｆｉｘｅｄｐｏｉｎｔｔｈｅｏｒｅｍｓａｎｄｃｏｉｎｃｉｄｅｎｃｅｔｈｅｏｒｅｍｓｉｎｖｏｌｖｉｎｇｓｏ＿ｃａｌｅｄＫａｋｕｔａｎｉｆａｃｔｏｒｉｚａｂｌ...     

SYSTEM OF COINCIDENCE THEOREMS IN PRODUCT TOPOLOGICAL SPACES AND APPLICATIONS (Ⅱ)

By applying coincidence theorems in part (Ⅰ) for two families of set-valued mappings defined on product space of noncompact FC-spaces in preceding paper, some new existence theorems for system of vector equilibrium problems, system of inequalities and system of minimax theorems were established in FC-spaces. These results generalize some known results in recent literature.     

Fixed point index of ultimately compact set-valued mappings in Hausdorff locally convex spaces and its applications

The author defines a concept of fixed point index of ultimately compact set-valued mappings in Hausdorff locally convex spaces. Using this concept, the author establishes several nonzero fixed point theorems of set-valued -condensing mappings. These theorems extend some known results in [1,2,7,8,9].Projects Supported by the Science Fund of the Chinese Academy of Sciences     

MAXIMAL ELEMENTS OF A FAMILY OF GB-MAJORIZED MAPPINGS IN PRODUCT FC-SPACES AND APPLICATIONS

A new family of GB-majorized mappings from a topological space into a finite continuous topological spaces （in short, FC-space） involving a better admissible set-valued mapping is introduced. Some existence theorems of maximal elements for the family of GB-majorized mappings are proved under noncompact setting of product FCspaces. Some applications to fixed point and system of minimax inequalities are given in product FC-spaces. These theorems improve, unify and generalize many important results in recent literature.     

Fixed point index of uniform limit of set-Valued strict set-contractive mappings and its applications

In this paper,the class of uniform limit mappings of set-valued,strick set-contractivemappings is discussed.Furthermore,the fixed point index theory for the uniform limitmappings is established.Using the fixed point index theory,some positive fixed pointtheorems are proved.Our theorems generalize some results in[1,4,5,7].     

Nonempty intersection theorems in topological spaces with applications

In this paper, we establish some new nonempty intersection theorems for generalized L-KKM mappings and prove some new fixed point theorems for set-valued mappings under suitable conditions in topological spaces. As applications, an existence theorem for an equilibrium problem with lower and upper bounds and two existence theorems for a quasi-equilibrium problem with lower and upper bounds are obtained in topological spaces. Our results generalize some known results in the literature.     

Existence and stability of common fixed points for systems of mappings

In this paper,we establish some common fixed point theorems and stability theorems of the sets of common fixed points for the systems of set-valued and single-valued nonlinear contractive type mappings in a finite Cartesian product of metric spaces.     

Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications （I）

First, the notions of the measure of noncompactness and condensing set-valued mappings are introduced in locally FC-uniform spaces without convexity structure. A new existence theorem of maximal elements of a family of set-valued mappings involving condensing mappings is proved in locally FC-uniform spaces. As applications, some new equilibrium existence theorems of generalized game involving condensing mappings are established in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Some further applications of our results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper. Project supported by the Natural Science Foundation of Sichuan Education Department of China (Nos. 2003A081 and SZD0406)     

Caristi type hybrid fixed point theorems in menger probabilistic metric space

I.IntroductionandPreliminariesInl976,CaristiprovedtheCaristi'sfixedpointtheoreminIll.Becausethistheoremdoesnotrequirethecontinuityofthemapping.ittindsapplicationsinmanyfields.Inl99l,S.S.Changetal.l'l,broughtforwardCaristi'sfixedpointtheoremandEkeland'svar…     

Random directional contractors and their applications

In this paper, as the generalizations of Altman’s directional contractors[4,5] and Lee and Padgett’s random contractors[1,2] we introduce the concept of random directional contractors for set-valued random operators. Using the new concept and transfinite induction, we show several existence theorems to solutions of nonlinear set-valued random operator equations. Our theorems improve and generalize the corresponding results in [1,2,4,5,11]. Next, some applications of our results to nonlinear random integral and differential equations are given.     

CONSTRAINED MULTIOBJECTIVE GAMES IN LOCALLY CONVEX H-SPACES

IntroductionTheconceptofanequilibriumpointforann_persongamewasfirstintroducedbyNash[1,2 ],whoestablishedtheexistenceoftheequilibriumpointundercertainassumptions.Sincethen ,theNashequilibriumproblemforn_persongameshavebeenintensivelystudiedandextendedbyanumberofauthorsundervariousassumptionsanddifferentdirections.Theconstrainedgameswithfiniteorinfiniteplayersisanimportantgeneralizationofn_persongameswhichhavebeenwidelystudiedbymanyauthors.Recently ,muchattentionhasbeenfocusedonthegameproblemsw…     

Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications (Ⅰ)

First, the notions of the measure of noncompactness and condensing setvalued mappings are introduced in locally FC-uniform spaces without convexity structure. A new existence theorem of maximal elements of a family of set-valued mappings involving condensing mappings is proved in locally FC-uniform spaces. As applications,some new equilibrium existence theorems of generalized game involving condensing mappings are established in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Some further applications of our results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper.     

New collectively fixed point theorems and applications inG-convex spaces

By applying the technique of continuous partition of unity and Tychonoff’s fixed point theorem, some new collectively fixed point theorems for a family of set-valued mappings defined on the product space of noncompact G-convex spaces are proved. As applications, some nonempty intersetion theorems of Ky Fan type for a family of subsets of the product space of G-convex spaces are proved; An existence theorem of solutions for a system of nonlinear inequalities is given in G-convex spaces and some equilibrium existence theorems of abstract economies are also obtained in G-convex spaces. Our theorems improve, unify and generalized many important known results in recent literature.     

Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications(Ⅱ)

This paper is a continuum of the preceding paper of author.Some new sys- tems of generalized vector quasi-equilibrium problems involving condensing mappings are introduced and studied in locally FC-uniform spaces.By applying the existence theorem of maximal elements of condensing set-valued mappings in locally FC-uniform spaces obtained by author in the preceding paper,some new existence theorems of solutions for the systems of generalized vector quasi-equilibrium problems are proved in locally FC- uniform spaces.These results improve and generalize some known results in literature to locally FC-uniform spaces.     

Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications (Ⅱ)

This paper is a continuum of the preceding paper of author. Some new systems of generalized vector quasi-equilibrium problems involving condensing mappings are introduced and studied in locally FC-uniform spaces. By applying the existence theorem of maximal elements of condensing set-valued mappings in locally FC-uniform spaces obtained by author in the preceding paper, some new existence theorems of solutions for the systems of generalized vector quasi-equilibrium problems are proved in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces.     

Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications(Ⅰ)

First,the notions of the measure of noncompactnees and condensing set- valued mappings are introduced in locally FC-uniform spaces without convexity struc- ture.A new existence theorem of maximal elements of a family of set-valued mappings involving condensing mappings is proved in locally FC-uniform spaces.As applications, some new equilibrium existence theorems of generalized game involving condensing map- pings are established in locally FC-uniform spaces.These results improve and generalize some known results in literature to locally FC-uniform spaces.Some further applications of our results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper.