Coupled Coincidence Point Results for (ψ, α, β)‐Weak Contractions in Partially Ordered Metric Spaces

Abstract

In this paper coupled coincidence points of mappings satisfying a nonlinear contractive condition in the framework of partially ordered metric spaces are obtained. Our results extend the results of Harjani et al. (2011). Moreover, an example of the main result is given. Finally, some coupled coincidence point results for mappings satisfying some contraction conditions of integral type in partially ordered complete metric spaces are deduced.

Multidimensional Fixed Point Results for Contraction Mapping Principle With Application

“…As an application of our result we study the existence and uniqueness of the solution to an integral equation. We improve and generalize the results of Alsulami [1], Razani and Parvaneh [15], Su [20] and many other famous results in the literature.…”

GENERALIZED (Ψ, Θ, Φ)-Contraction WITH APPLICATION TO ORDINARY DIFFERENTIAL EQUATIONS

“…They also established some coupled fixed point theorems, which eectionxtend and generalized the results of Harjani et al [17], Gnana-Bhaskar and Lakshmikantham [6] and Luong and Thuan [23]. In the last s, they gave unique coupled coincidence point theorems without using compatibility, which extend and generalized the results of Alotaibi and Alsulami [3], Alsulami [4], Lakshmikantham and Ciric [22] and Razani and Parvaneh [32]. For more details one can consult ( [1], [2], [5], [9]- [12], [14], [16], [19], [24], [25], [27], [29]- [35]).…”

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

“…Furthermore, we show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem. We modify, improve, sharpen, enrich and generalize the results of Alotaibi and Alsulami [1], Alsulami [2], Gnana-Bhaskar and Lakshmikantham [6], Harjani and Sadarangani [13], Harjani et al [14], Lakshmikantham and Ciric [22], Luong and Thuan [23], Nieto and Rodriguez-Lopez [26], Ran and Reurings [27], Razani and Parvaneh [28] and many other famous results in the literature.…”

“…They also illustrated these results by proving the existence and uniqueness of the solution for periodic boundary value problems. A large number of authors established coupled fixed/coincidence point theorems by using this notion in different context, (see [1], [2], [3], [8], [9], [10], [15], [16], [23], [24], [28], [33], [35], [36]). Inspired by these papers, Berinde and Borcut [4] defined tripled fixed points and established some tripled fixed point theorems.…”