Unified multi-tupled fixed point theorems involving mixed monotone property in ordered metric spaces

TL;DR

This paper introduces a unified framework for multi-tupled fixed point theorems in ordered metric spaces, extending classical results to include various types like coupled, tripled, and quadrupled fixed points using Boyd-Wong contractions.

Contribution

It presents a unified approach to multi-tupled fixed points, generalizing and unifying several existing fixed point theorems in the literature.

Findings

Established existence and uniqueness of multi-tupled fixed points.

Unified several classical fixed point results under one framework.

Extended fixed point theory to Boyd-Wong type contractions with mixed monotone property.

Abstract

In the present article, we introduce a unified notion of multi-tupled fixed points and utilize the same to prove some existence and uniqueness unified multi-tupled fixed point theorems for Boyd-Wong type nonlinear contractions satisfying generalized mixed monotone property in ordered metric spaces. Our results unify several classical and well-known n-tupled (including coupled, tripled and quadrupled ones) fixed point results existing in the literature.