A generalization of Matkowski's fixed point theorem and Istratescu's fixed point theorem concerning convex contractions

TL;DR

This paper generalizes Matkowski's and Istratescu's fixed point theorems for convex contractions within b-metric spaces, broadening their applicability and demonstrating effectiveness through examples.

Contribution

It introduces a unified generalization of two classical fixed point theorems for convex contractions in b-metric spaces, with illustrative examples.

Findings

Successful generalization of fixed point theorems

Effective application demonstrated through examples

Broader framework for convex contractions

Abstract

In this paper we obtain a generalization of Matkowski's fixed point theorem and Istratescu's fixed point theorem concerning convex contractions in the framework of b-metric spaces. By providing appropriate examples we show that the above mentioned two generalizations are effective.