Some Common Fixed Point Theorems for Weakly Compatible Mappings in Metric Spaces

M A Ahmed

doi:10.1155/2009/804734

Abstract

AbstractWe establish a common fixed point theorem for weakly compatible mappings generalizing a result of Khan and Kubiaczyk (1988). Also, an example is given to support our generalization. We also prove common fixed point theorems for weakly compatible mappings in metric and compact metric spaces.

Highlights

In the last years, fixed point theorems have been applied to show the existence and uniqueness of the solutions of differential equations, integral equations and many other branches mathematics see, e.g., 1–3
We are concerned with the following: 1 replacing the commutativity of the mappings in Theorem 1.10 by the weak compatibility of a pair of mappings to obtain a common fixed point theorem metric spaces without the continuity assumption of the mappings, 2 giving an example to support our generalization of Theorem 1.10, 3 establishing another common fixed point theorem for two families of set-valued mappings and two single-valued mappings, 4 proving a common fixed point theorem for weakly compatible mappings under a strict contractive condition on compact metric spaces
We establish a common fixed point theorem in metric spaces generalizing Theorems 1.10

Summary

Research Article

Some Common Fixed Point Theorems for Weakly Compatible Mappings in Metric Spaces. We establish a common fixed point theorem for weakly compatible mappings generalizing a result of Khan and Kubiaczyk 1988. An example is given to support our generalization. We prove common fixed point theorems for weakly compatible mappings in metric and compact metric spaces.

Introduction

Main Results

This contradiction demands that