# A new approach to coincidence and common fixed points under a homotopy of families of mappings in $b$-metric spaces

## TL;DR

This paper introduces a novel method for establishing coincidence and common fixed points for families of mappings in preordered b-metric spaces using order homotopies, expanding fixed point theory in generalized metric spaces.

## Contribution

It presents new fixed point theorems under order homotopies in preordered b-metric spaces, a significant extension of existing fixed point results.

## Key findings

- Established coincidence fixed point results under order homotopies.
- Extended fixed point theory to preordered b-metric spaces.
- Provided conditions for the existence of common fixed points.

## Abstract

In this paper we derive coincidence and common fixed point results under order homotopies of families of mappings in preordered $b$-metric spaces.