Coupled coincidence points for mixed monotone operators in partially ordered metric spaces

Abstract

In this paper, we give and prove some coupled coincidence point theorems for mappings F : X × X → X and g : X → X in partially ordered metric space X, where F has the mixed g-monotone property. Our results improve and generalize the results of Bhaskar and Lakshmikantham (Nonlinear Anal

Coupled Coincidence Points for Mixed Monotone Random Operators in Partially Ordered Metric Spaces

“…In this section, we study coupled random coincidence and coupled random fixed point theorems for a pair of random mappings : Ω × ( × ) → and : Ω × → . Then we will prove some results for random mixed monotone mappings, which are the extensions of corresponding results for deterministic mixed monotone mappings of Karapınar et al [17].…”

“…Moreover coupled random coincidence results in partially ordered complete metric spaces were considered in [20][21][22]. Following Karapınar et al [17] and Shatanawi and Mustafa [21], we improve these results for a pair of compatible mixed monotone random mappings : Ω × ( × ) → and : Ω × → , where and satisfy some weak contractive conditions. Presented results are also referred to the extensions and improve the corresponding results in [19,21] and many other authors' work.…”

“…Theorem 4 (see [17]). Let ( , ≤) be a partially ordered set and suppose that there exists a metric on such that ( , ) is a complete metric space.…”

“…Fixed point theorems for monotone operators in ordered Banach spaces have been investigated and found various applications. Since then, fixed point theorems for mixed monotone mappings in partially ordered metric spaces are of great importance and have been utilized for matrix equations, ordinary differential equations, and the existence and uniqueness of solutions for some boundary value problems (see [9][10][11][12][13][14][15][16][17]).…”

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.…”