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

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 [M. Choban, V. Berinde, A general concept of multiple fixed point for mappings defined on spaces with a distance, Carpathian J. Math. 33 (2017), no. 3, 275--286] and also simplifies some concepts of multiple fixed point considered by various authors in the last decade or so.

Keywords

• distance space
• partial order
• symmetric space
• quasi-metric space
• $H$-distance
• contraction condition
• multiple fixed point.