Abstract
The main purpose of this paper is to establish a new collectively fixed point theorem in noncompact abstract convex spaces. As applications of this theorem, we obtain some new existence theorems of equilibria for generalized abstract economies in noncompact abstract convex spaces.
Highlights
Fixed point theorems for a family of set-valued mappings play a vital role in studying various nonlinear problems
The main purpose of this paper is to establish a new collectively fixed point theorem in noncompact abstract convex spaces
In 1991, Tarafdar [1] established a collectively fixed point theorem in topological vector spaces and gave applications to mathematical economies, game theory, and problems of social sciences
Summary
Fixed point theorems for a family of set-valued mappings play a vital role in studying various nonlinear problems. In 1991, Tarafdar [1] established a collectively fixed point theorem in topological vector spaces and gave applications to mathematical economies, game theory, and problems of social sciences. A lot of generalizations and applications of collectively fixed point theorem under different assumptions and different underlying spaces have been studied by many authors (see [2,3,4,5,6,7] and the references therein). Inspired and motivated by the above results, in this paper, we establish a new collectively fixed point theorem in noncompact abstract convex spaces. As applications of this fixed point theorem, some new existence theorems of equilibria for generalized abstract economies are proved under the setting of noncompact abstract convex spaces
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