Weak contractions via $\lambda$-sequences

TL;DR

This paper investigates fixed points of self-maps in metric type spaces using weak contraction conditions, employing $5$-sequences and real-valued maps, with implications for quasi-pseudometric spaces.

Contribution

It introduces a novel approach using $5$-sequences and real-valued maps to establish fixed point results in metric type spaces.

Findings

Established fixed point theorems for weakly contractive mappings.

Extended results to quasi-pseudometric type spaces.

Provided new implications for self-mappings in these spaces.

Abstract

In this note, we discuss common fixed point for a family of self mapping defined on a metric type space and satisfying a weakly contractive condition. In our development, we make use of the $\lambda$-sequence approach and also of a certain class of real valued maps. We derive some implications for self-mappings on quasi-pseudometric type spaces.