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

TL;DR

This paper introduces a generalized monotone property in ordered metric spaces and proves unified fixed point theorems for multi-tupled mappings, encompassing classical results like coupled and tripled fixed points.

Contribution

It presents a unified framework for multi-tupled fixed point theorems, extending and unifying several classical results in the literature.

Findings

Established existence and uniqueness of multi-tupled fixed points

Unified various classical fixed point theorems under a generalized framework

Applicable to nonlinear contraction mappings with monotone property

Abstract

In this paper, we introduce a generalized notion of monotone property and prove some results regarding existence and uniqueness of multi-tupled fixed points for nonlinear contraction mappings satisfying monotone property in ordered complete metric spaces. Our results unify several classical and well known n-tupled (including coupled, tripled and quadruple ones) fixed point results existing in literature.