On coincidence and common fixed point theorems of eight self-maps satisfying an FM-contraction condition

Mi Zhou,Adrian Secelean,Xiao-Lan Liu

doi:10.15388/na.2019.6.9

Abstract

In this paper, a new type of contraction for several self-mappings of a metric space, called FM-contraction, is introduced. This extends the one presented for a single map by Wardowski [Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012:94, 2012]. Coincidence and common fixed point of eight self mappings satisfying FM-contraction conditions are established via common limit range property without exploiting the completeness of the space or the continuity of the involved maps. Coincidence and common fixed point of eight self-maps satisfying FM-contraction conditions via the common property (E.A.) are also studied. Our results generalize, extend and improve the analogous recent results in the literature, and some examples are presented to justify the validity of our main results.

Highlights

Using a function F satisfying three conditions (F1)–(F3), Wardowski [22] introduced a new concept of F -contraction for a single-valued self map of a complete metric space and proved that every F -contraction possesses a unique fixed point
We utilize the common property (E.A.) instead of (CLR(AB)(ST )) property of (Lf, AB) and (M g, ST ) in Theorem 2 in order to obtain coincidence and common fixed point results for eight self-maps
We present some examples to support our main results

Summary

Introduction

Using a function F satisfying three conditions (F1)–(F3), Wardowski [22] introduced a new concept of F -contraction for a single-valued self map of a complete metric space and proved that every F -contraction possesses a unique fixed point. The aim of this paper is to establish the existence and uniqueness of coincidence and common fixed point of eight self-maps in a (noncomplete) metric spaces satisfying a new type contraction condition, called FM -contraction via common (CLR(AB)(ST )) property or common property (E.A.). The new type FM -contraction defined by us is more comprehensive than the one introduced by Piri and Kumam [11] and Wardowski [22]

Preliminaries

Main results

Conclusion