Weakly contractive maps in altering metric spaces

TL;DR

This paper explores fixed point results for weakly contractive maps in altering metric spaces, showing their relation to existing results and extending these concepts further.

Contribution

It demonstrates that weakly contractive fixed point results are closely related to altering metric fixed point theorems and provides new extensions of these results.

Findings

Weakly contractive fixed point results are nearly covered by altering metric theorems.

Extensions of fixed point results for weakly contractive maps are proposed.

The paper clarifies the relationship between different types of contractive mappings.

Abstract

The weakly contractive metric type fixed point result in Berinde [Nonlinear Anal. Forum, 9 (2004), 45-53] is "almost" covered by the related altering metric one due to Khan et al [Bull. Austral. Math. Soc., 30 (1984), 1-9]. Further extensions of these statements are then provided.