Fixed Point Theorems In Ordered Partial b-Metric Spaces With New Setting

TL;DR

This paper introduces new fixed point theorems in ordered partial b-metric spaces by defining partial completeness and a novel contraction, enabling fixed point existence proofs in incomplete spaces.

Contribution

It presents new concepts like partial completeness and a new contraction type, extending fixed point theory to incomplete metric spaces with non-contractive maps.

Findings

Fixed points exist in incomplete metric spaces under new conditions

Introduction of partial completeness as a new concept

Validation through an illustrative example

Abstract

The main purpose of this paper is to find the fixed point in such cases where existing literature remain silent. In this paper we introduce partial completeness, a new type of contraction and many other definitions. Using this approach the existence of fixed point can be proved in incomplete metric spaces with non-contraction map on it. We have reported an example in support our result.