Some generalizations of common fixed point problems with applications

Zhe Yang

doi:10.1186/1687-1812-2014-189

Abstract

In this paper, we establish a unified approach to study the existence of fixed points for common fixed point problems. Moreover, we introduce mixed systems of common fixed point problems, systems of common fixed point problems and common fixed point problems without convex assumptions. As applications, we establish a general type of some set-valued variational inequalities, and we obtain some existence theorems of solutions of set-valued variational inequalities. The results of this paper improve and generalize several known results on common fixed point problems.

Highlights

1 Introduction In three recent papers [ – ], by using some new concepts of generalized KKM mappings, the authors established common fixed point theorems for families of set-valued mappings in Hausdorff topological vector spaces
Motivated and inspired by research works mentioned above, in this paper, we establish a unified approach to study the existence of fixed points for common fixed point problems
We introduce a new class of problems, called mixed systems of common fixed point problems (MSCFP)

Summary

Introduction

In three recent papers [ – ], by using some new concepts of generalized KKM mappings, the authors established common fixed point theorems for families of set-valued mappings in Hausdorff topological vector spaces.

Results

Conclusion