Rectangular metric like type spaces and fixed points

TL;DR

This paper introduces rectangular metric-like spaces and modified metric-like spaces, establishing fixed point theorems and topological properties, supported by examples to demonstrate their applications.

Contribution

It presents new types of metric spaces, extending fixed point theory and topology, with proofs and illustrative examples.

Findings

Fixed point theorems under contraction principles

Topological and convergence properties of new spaces

Examples demonstrating the applicability of the introduced spaces

Abstract

In this paper we introduce the concept of the rectangular metric like spaces, along with its topology and we prove some fixed point theorems under different contraction principles. We introduce the concept of modified metric-like space as well and prove some topological and convergence properties under the symmetric convergence. Some examples are given to illustrate the proven results and enrich the new introduced metric type spaces.