Common fixed points of mappings satisfying implicit contractive conditions

Vasile Berinde,Francesca Vetro

doi:10.1186/1687-1812-2012-105

Abstract

In this article we obtain, in the setting of metric spaces or ordered metric spaces, coincidence point, and common fixed point theorems for self-mappings in a general class of contractions defined by an implicit relation. Our results unify, extend, generalize many related common fixed point theorems from the literature. Mathematics Subject Classification (2000): 47H10, 54H25.

Highlights

Introduction and preliminariesIt is well known that the contraction mapping principle, formulated and proved in the Ph.D. dissertation of Banach in 1920, which was published in 1922 [1], is one of the most important theorems in classical functional analysis
Several classical fixed point theorems and common fixed point theorems have been recently unified by considering general contractive conditions expressed by an implicit relation, see Popa [16,17] and Ali and Imdad [18]
In [21], Berinde obtained some constructive fixed point theorems for almost contractions satisfying an implicit relation

Summary

Introduction

Introduction and preliminariesIt is well known that the contraction mapping principle, formulated and proved in the Ph.D. dissertation of Banach in 1920, which was published in 1922 [1], is one of the most important theorems in classical functional analysis. In [21], Berinde obtained some constructive fixed point theorems for almost contractions satisfying an implicit relation. In this article we obtain, in the setting of metric spaces or ordered metric spaces, coincidence point, and common fixed point results for self-mappings in a general class of contractions defined by an implicit relation.

Results

Conclusion