Multiple fixed point theorems for contractive and Meir-Keeler type mappings defined on partially ordered spaces with a distance

TL;DR

This paper introduces a new general concept of multiple fixed points for mappings on partially ordered distance spaces, extending and simplifying previous theories with contraction and monotonicity conditions.

Contribution

It presents a unified framework for multiple fixed points in partially ordered metric spaces, enhancing existing results with broader applicability and simplified concepts.

Findings

Established new multiple fixed point theorems under contraction conditions

Extended previous results to more general partially ordered distance spaces

Simplified the conceptual framework for multiple fixed points

Abstract

We introduce and study a general concept of multiple fixed point for mappings defined on partially ordered distance spaces in the presence of a contraction type condition and appropriate monotonicity properties. This notion and the obtained results complement the corresponding ones from [Choban, M., Berinde, V., {\it A general concept of multiple fixed point for mappings defined on spaces with a distance} (submitted)] and also simplifies some concepts of multiple fixed point considered by various authors in the last decade or so.