On almost coincidence points in generalized convex spaces

Zoran D Mitrović

doi:10.1155/fpta/2006/91397

Abstract

We prove an almost coincidence point theorem in generalized convex spaces. As an application, we derive a result on the existence of a maximal element and an almost coincidence point theorem in hyperconvex spaces. The results of this paper generalize some known results in the literature.

Highlights

Introduction and preliminariesThe notion of a generalized convex space we work with in this paper was introduced by Park and Kim in [10]
We prove an almost coincidence point theorem in generalized convex spaces
We obtain an almost coincidence point theorem in generalized convex spaces

Summary

Introduction and preliminaries

The notion of a generalized convex space we work with in this paper was introduced by Park and Kim in [10]. Many results on fixed points, coincidence points, equilibrium problems, variational inequalities, continuous selections, saddle points, and others have been obtained, see, for example, [6, 8, 10,11,12,13]. We obtain an almost coincidence point theorem in generalized convex spaces. Some applications to the existence of a maximal element of an almost fixed point theorem in hyperconvex spaces are given. For any B ⊂ Y , the lower inverse and upper inverse of B under F are defined by. A map F : X Y is continuous if and only if it is upper and lower semicontinuous.

On almost coincidence points

Almost-like coincidence point theorem

Almost coincidence point theorem in metrizable G-convex spaces