The class of ( α , ψ ) $(\alpha,\psi)$ -type contractions in b-metric spaces and fixed point theorems

Bessem Samet

doi:10.1186/s13663-015-0344-z

Abstract

We study the existence and uniqueness of fixed points for self-operators defined in a b-metric space and belonging to the class of $(\alpha,\psi)$ -type contraction mappings. The obtained results generalize and unify several existing fixed point theorems in the literature.

Highlights

1 Introduction and preliminaries Very recently, we studied in [ ] the existence and uniqueness of fixed points for selfoperators defined in a metric space and belonging to the class of (α, ψ)-type contraction mappings
We proved that the class of α-ψtype contractions includes large classes of contraction-type operators, whose fixed points can be obtained by means of the Picard iteration
The aim of this paper is to extend the obtained results in [ ] to self-operators defined in a b-metric space

Summary

Introduction

Introduction and preliminariesVery recently, we studied in [ ] the existence and uniqueness of fixed points for selfoperators defined in a metric space and belonging to the class of (α, ψ)-type contraction mappings (see [ – ] for some works in this direction). Our first main result is the following fixed point theorem which requires the continuity of the mapping T.

Objectives

Results

Conclusion