# Chatterjea type fixed point in Partial $b$-metric spaces

## TL;DR

This paper establishes new fixed point theorems of Chatterjea type in partial $b$-metric spaces, extending classical contraction principles and exploring stability and completion properties.

## Contribution

It introduces fixed point theorems of Chatterjea type in partial $b$-metric spaces and extends the Banach contraction principle in this context.

## Key findings

- Proved Chatterjea type fixed point theorems in partial $b$-metric spaces.
- Extended Banach contraction principle to partial $b$-metric spaces.
- Verified $T$-stability of Picard's iteration and discussed the $P$ property.

## Abstract

In this paper, we give and prove two Chatterjea type fixed point theorems on partial $b$-metric space. We propose an extension to the Banach contraction principle on partial $b$-metric space which was already presented by Shukla and also study some related results on the completion of a partial metric type space. In particular, we prove a joint Chatterjea-Kannan fixed point theorem. We verify the $T$-stability of Picard's iteration and conjecture the $P$ property for such maps. We also give examples to illustrate our results.