# New coincidence point and fixed point theorems for essential distances and $e^{0}$-metrics

## TL;DR

This paper introduces new fixed point and coincidence point theorems for essential distances and $e^{0}$-metrics, generalizing and improving several classical fixed point results and principles in metric space theory.

## Contribution

It presents novel theorems that extend existing fixed point results to essential distances and $e^{0}$-metrics, broadening their applicability.

## Key findings

- Generalized fixed point theorems for essential distances and $e^{0}$-metrics
- Improved upon classical fixed point theorems
- Unified various fixed point principles in a broader framework

## Abstract

In this paper, we establish some new fixed point theorems and coincidence point theorems for essential distances and $e^{0}$-metrics which generalize and improve Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, Nadler's fixed point theorem and Banach contraction principle and many known results in the literature.