Meir-Keeler Type Multidimensional Fixed Point Theorems in Partially Ordered Metric Spaces

Abstract

We study the existence and uniqueness of a fixed point of the multidimensional operators which satisfy Meir-Keeler type contraction condition. Our results extend, improve, and generalize the results mentioned above and the recent results on these topics in the literature.

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

“…After these starting papers, a substantial number of articles were dedicated to the study of triple fixed points, quadruple fixed points, as well as to multiple fixed points (also called fixed point of m-order, or "a multidimensional fixed point", or "an m-tuplet fixed point", or "an m-tuple fixed point"), see [1], [2], [7], [48], [49], [50], [53], [60], [67]- [72], [81], [83], [86], which form a very selective list contributions.…”

Multidimensional coincidence point results for generalized $(\psi ,\theta ,\varphi)$-contraction on ordered metric spaces

“…However, they used permutations of variables and distinguished between the first and the last variables. For more details one can refer ( [11], [18], [19], [20], [21], [22], [26], [30], [31], [32], [34], [38]). In this research paper, we obtain some coincidence point theorem for g-non-decreasing mappings under generalized (ψ, θ , φ)-contraction on a partially ordered metric space.…”

Some new fixed point theorems under $$(\mathcal {A},\mathcal {S})$$ ( A , S ) -contractivity conditions

“…Such family let them to consider a wide family of contractions, called R-contractions, that unify, under the same axioms, many different classes of contractions as the following ones: Z-contractions, manageable contractions, Meir and Keeler contractions [6,12,14,15], Geraghty's contractions [10], Dutta and Choudhury's contractions [9], etc.…”