Fixed point results on \theta-metric spaces via simulation functions

TL;DR

This paper extends fixed point theory to heta-metric spaces using simulation functions, introducing modified Z-contractions and establishing existence and uniqueness of fixed points with illustrative examples.

Contribution

It generalizes fixed point results to heta-metric spaces, introduces modified Z-contractions, and connects these concepts with existing theories.

Findings

Established fixed point existence and uniqueness for modified Z-contractions.

Extended the class of contraction mappings in heta-metric spaces.

Provided examples illustrating the main theoretical results.

Abstract

In a recent article, Khojasteh et al. introduced a new class of simulation functions, Z-contractions, with blending over known contractive conditions in the literature. Subsequently, in this paper, we extend and generalize the results on \theta-metric context and we discuss some fixed point results in connection with existing ones. Also, we originate the notion of modified Z-contractions and explore the existence and uniqueness of fixed points of such functions on the said spaces. Finally we include examples to instantiate our main results.