MAXIMAL ELEMENTS OF A FAMILY OF G_B-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.

MAXIMAL ELEMENTS FOR G_B-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.

MAXIMAL ELEMENTS FOR G_B-MAJORIZED MAPPINGS IN PRODUCT G_CONVEX SPACES AND APPLICATIONS (Ⅱ)

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.

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.

MAXIMAL ELEMENTS AND EQUILIBRIUM OF ABSTRACT ECONOMY

An existence theorem of maximal elements for a new type of preference correspondences which are Q(0)-majorized is given. Then some existence theorems of equilibrium for abstract economy and qualitative game in which the constraint or preference correspondences are Q(0)-majorized are obtained in locally convex topological vector spaces.

AN EXISTENCE THEOREM FOR MAXIMAL ELEMENTS AND ITS APPLICATIONS

An existence theorem of maximal elements for an L＊-majorized correspondence defined on a non-paracompact H-space is established. As applications of the result, an equilibrium existence theorem for a non-paracompact generalized game in H-spaces with infinitely many players and with L＊-majorized correspondences is given.

MAXIMAL ELEMENTS OF CONDENSING PREFERENCE MAPS IN LOCALLY CONVEX HAUSDORFF SPACES

Two existence theorems of maximal elements of condensing preference maps in locally convex Hausdorff spaces are proved which generalize the recent results of Mehta. One of them positively answers the open problem mentioned by Mehta.

SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS ON PRODUCT FC-SPACES

By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.

NEW SYSTEMS OF GENERALIZED QUASI-VARIATIONAL INCLUSIONS IN FC-SPACES AND APPLICATIONS

In this paper, we study some new systems of generalized quasi-variational inclusion problems in FC-spaces without convexity structure.By applying an existence theorem of maximal elements of set-valued mappings due to the author, some new existence theorems of solutions for the systems of generalized quasi-variational inclusion problems are proved in noncompact FC-spaces. As applications, some existence results of solutions for the system of quasi-optimization problems and mathematical programs with the systems of generalized quasi-variational inclusion constraints are obtained in FC-spaces.

COINCIDENCE THEOREMS INVOKING COMPOSITES OF ACYCLIC MAPPINGS AND APPLICATIONS

Some new coincidence theorems involving a new class of set-valued mappingscontaining composites of acyclic mappings defined on a contractible space are proved.As applications, some existence theorems of maximal elements and solutions of abstract variational inequalities, and best approximation theorems are proved. These theorems improve and generalize a number of known results in recent literature.

MATHEMATICAL PROGRAMS WITH SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM CONSTRAINTS IN FC-SPACES

In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci（x）-FC-partially diagonally quasiconvex, Ci（x）-FC-quasiconvex, and Ci（x）-FC- quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.

A New Fixed Point Theorem in L-Convex Spaces with Applications

In this paper, we present a new fixed point theorem in L-convex spaces and apply it to obtain a maximal element theorem, a variational inequality and a saddle point theorem in L-convex spaces.

Alternative principles and minimax inequalities in G-convex spaces

Using a fixed point theorem by Kuo, Jeng and Huang, we obtain in G-convex spaces a very general intersection theorem concerning the values of three maps. From this result we derive successively alternative theorems concerning maximal elements, analytic alternatives and minimax inequalities.

GLOBAL OPTIMIZATION OF THE DIFFERENCE OF TWO INCREASING PLUS-CONVEX-ALONG-RAYS FUNCTIONS

The theory of increasing and convex-along-rays(ICAR)functions defined on a convex cone in a real locally convex topological vector space X was already well developed.In this paper,we first examine abstract convexity of increasing plus-convex-along-rays(IPCAR)functions defined on a real normed linear space X.We also study,for this class of functions,some concepts of abstract convexity,such as support sets and subdifferentials.Finally,as an application,we characterize the maximal elements of the support set of strictly IPCAR functions and give optimality conditions for the global minimum of the difference between two IPCAR functions.

Systems of generalized quasi-variational inclusion (disclusion) problems in FC-spaces

By applying an existence theorem of maximal elements of set-valued mappings in FC-spaces proposed by the author, some new existence theorems of solutions for systems of generalized quasi-variational inclusion （disclusion） problems are proved in FC-spaces without convexity structures. These results improve and generalize some results in recent publications from closed convex subsets of topological vector spaces to FC-spaces under weaker conditions.

A New GLKKM Theorem and Its Application to Abstract Economies

In this paper,a new GLKKM theorem in L-convex spaces is established.As applications,a new fixed point theorem and a maximal element theorem are obtained in Lconvex spaces.Finally,equilibrium existence theorems for economies and qualitative games in L-convex spaces are yielded.

Existence of Solutions to Generalized Vector Quasi-variational-like Inequalities with Set-valued Mappings

In this paper, we introduce and study a class of generalized vector quasivariational-like inequality problems, which includes generalized nonlinear vector variational inequality problems, generalized vector variational inequality problems and generalized vector variational-like inequality problems as special cases. We use the maximal element theorem with an escaping sequence to prove the existence results of a solution for generalized vector quasi-variational-like inequalities without any monotonicity conditions in the setting of locally convex topological vector space.

Classification about Non-Solvable Groups with Exactly 40 Maximal Order Elements

Let φ be a homomorphism from a group H to a group Aut（N）. Denote by Hφ× N the semidirect product of N by H with homomorphism φ. This paper proves that： Let G be a finite nonsolvable group. If G has exactly 40 maximal order elements, then G is isomorphic to one of the following groups： （1） Z4φ×A5, kerφ = Z2; （2） D8φ ×A5, kerφ = Z2 ×Z2; （3） G/N = S5, N = Z（G） = Z2; （4） G/N = S5, N = Z2 ×Z2, N∩Z（G） = Z2.

A New Fixed Point Theorem in Noncompact Hyperconvex Metric Spaces and Its Application to Saddle Point Problems

In this paper, a new fixed point theorem is established in noncompact hyperconvex metric spaces. As applications, a continuous selection and its fixed point theorem, an existence theorem for maximal elements, a Ky Fan minimax inequality and an existence theorem for saddle points are obtained.

A New Fixed Point Theorem in Noncompact L-Convex Metric Spaces with Applications to Minimax Inequalities and Saddle Points

In this paper,a new fixed point theorem is established in noncompact complete Lconvex metric spaces.As applications,a maximal element theorem,a minimax inequality and a saddle point theorem are obtained.