Coupled coincidence points for monotone operators in partially ordered metric spaces

Abstract

Using the notion of compatible mappings in the setting of a partially ordered metric space, we prove the existence and uniqueness of coupled coincidence points involving a (j, ψ)-contractive condition for a mappings having the mixed g-monotone property. We illustrate our results with the help of an example.

Coupled and tripled coincidence point results without compatibility

“…Binayak et al [7] generalized these results to a pair of compatible maps. Recently, Alotaibi and Alsulami [8] extended the results in [5] for a compatible pair. Very recently, Borcut and Berinde [9] proved tripled coincidence point results for commuting maps.…”

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.…”

Tripled random coincidence point and common fixed point results of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras

“…Random coincidence point theorems are stochastic generalizations of classical coincidence point theorems, and play an important role in the theory of random differential and integral equations. Random fixed point theorems for contractive mapping on complete separable metric space have been proved by several authors (see [4,12,19,25,26,36]). Ćirić [12] proved some coupled random fixed point and coupled random coincidence results in partially ordered metric spaces.…”

“…Ćirić [12] proved some coupled random fixed point and coupled random coincidence results in partially ordered metric spaces. Afterwards, many coupled random coincidence results in partially ordered metric spaces were considered (see [4,19,36]). In this paper, by the concept of cone b-metric space over Banach algebra introduced by [17], we obtain tripled common random fixed point and tripled random fixed point theorems with several generalized Lipschitz constants in cone b-metric spaces over Banach algebras by omitting the normality of cones.…”