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.2010 MSC: 47H10; 47H09.

A Multiple Fixed Point Result for θ , ϕ , ψ -Type Contractions in the Partially Ordered Rashid1, Kalsoom2, Ghaffar3 et al. 2022Journal of Function Spaces

“…The abovementioned ideas serve as motivation of the work in the present paper. We have extended the results of [10] for partially ordered s-distance space, in terms of a significant multiple FP result under ðθ, ϕ, ψÞ-type contractive condition [13]. In support of this result, an example is also given.…”

“…In 2016, Choban and Berinde [10] generalized metric spaces to distance spaces. They established multidimensional FP results for ordered spaces with distance under certain contractive conditions [4,11].…”

Solution of Integral Equations Using Some Multiple Fixed Point Results in Special Kinds of Distance Spaces

“…In 2016, Choban [13] introduced a new concept of distance spaces, and Berinde and Choban [14,15] further studied ordered distance spaces satisfying certain contraction conditions for the multidimensional fixed points. Ansari et al introduced the concept of Cand inverse C-class distance in [16,17].…”

Multidimensional fixed points in generalized distance spaces

“…In 2016, Choban [2] generalized metric spaces as distance spaces. In 2017, Choban and Berinde [3,4] established multidimensional fixed point results for distance spaces in the presence of certain contractive condition. In this paper we provide some useful remarks with examples regarding distance spaces and establish multidimensional fixed point results for C-distance spaces with generalized contractive conditions.…”