Fixed point theorems for self and non-self F-contractions in metric spaces endowed with a graph

Awais Younus,Muhammad Asif,Muhammad Umer Azam

doi:10.1186/s42787-020-00100-9

Abstract

The main results obtained in this paper are fixed point theorems for self and non-self GF-contractions on metric spaces endowed with a graph. Our new results are generalization of recently fixed point theorems for self mappings on metric spaces and also fixed point theorems for non-self mappings in Banach spaces by using the concept of new type of contractive mappings namely F-contractions.

Highlights

The well-known Banach contraction theorem [1] has plenty of extensions in the literature
Jachymski [15, Theorem 3.2] generalized the Banach contraction theorem for self-mappings on complete metric spaces endowed with the graph, where as Berinde [16, Theorem 3.1] for non-self mappings to Banach spaces endowed with a graph by using the inwardness condition defined in [17]
We present a few preliminary notations and our main aim is to study the fixed point theorems for self-mappings as well as non-self mappings using F-contractions for metric spaces endowed with a graph

Summary

Introduction

The well-known Banach contraction theorem [1] has plenty of extensions in the literature (see, for example, [2, 3]). There are few other fixed point theorems for non-self mappings to Banach spaces endowed with a graph , see, for example, [18] and [19]. We present a few preliminary notations and our main aim is to study the fixed point theorems for self-mappings as well as non-self mappings using F-contractions for metric spaces endowed with a graph.

Results

Conclusion