On Approximate Coincidence Point Properties and Their Applications to Fixed Point Theory

Wei-Shih Du

doi:10.1155/2012/302830

Abstract

We first establish some existence results concerning approximate coincidence point properties and approximate fixed point properties for various types of nonlinear contractive maps in the setting of cone metric spaces and general metric spaces. From these results, we present some new coincidence point and fixed point theorems which generalize Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, and some well-known results in the literature.

Highlights

We present some new coincidence point and fixed point theorems which generalize Berinde-Berinde’s fixed point theorem, Mizoguchi-Takahashi’s fixed point theorem, and some well-known results in the literature
The set of coincidence point of g and T is denoted by COP g, T
We present some new coincidence point and fixed point theorems which generalize Berinde-Berinde’s fixed point theorem and Mizoguchi-Takahashi’s fixed point theorem

Summary

Introduction

It is known that every generalized multivalued almost g-contraction in a metric space X, d has the approximate coincidence point property provided each T x is g-invariant i.e., g T x ⊆ T x for each x ∈ X see 1, Theorem 2.7 .

Results

Conclusion