\theta-metric spaces: A generalization

TL;DR

This paper introduces heta-metric spaces, a generalization of metric spaces using a broader inequality, and explores their topological properties and fixed point theorems.

Contribution

It presents a new class of spaces called heta-metric spaces, extending traditional metric space concepts with generalized inequalities and establishing foundational properties and fixed point results.

Findings

Established topological properties of heta-metric spaces

Proved Banach and Caristi fixed point theorems in these spaces

Demonstrated the generalization encompasses traditional metric spaces

Abstract

In this paper, using a more generalized inequality instead of triangle inequality, the notion of \theta-metric space is introduced. Some important properties of induced topology by such spaces are presented. Also, Banach and Caristi type fixed point in such spaces are proved.