Quartet fixed point for nonlinear contraction

TL;DR

This paper introduces new theorems for quartet fixed points in nonlinear contractions using mixed g monotone mappings, expanding fixed point theory with practical examples.

Contribution

It presents novel quartet fixed point theorems utilizing mixed g monotone mappings, building on recent concepts of coupled and tripled fixed points.

Findings

New quartet fixed point theorems established

Examples provided to illustrate the results

Extension of fixed point theory to nonlinear contractions

Abstract

The notion of coupled fixed point is introduced in by Bhaskar and Lakshmikantham in [2]. Very recently, the concept of tripled fixed point is introduced by Berinde and Borcut [1]. In this manuscript, by using the mixed g monotone mapping, some new quartet fixed point theorems are obtained. We also give some examples to support our results.