Coupled fixed point results in cone metric spaces for "Equation missing" -compatible mappings

Abstract

In this paper, we introduce the concepts of w -compatible mappings, b-coupled coincidence point and b-common coupled fixed point for mappings F, G : X × X X, where (X, d) is a cone metric space. We establish b-coupled coincidence and bcommon coupled fixed point theorems in such spaces. The presented theorems generalize and extend several well-known comparable results in the literature, in particular the recent results of Abbas et al. [Appl. Math. Comput. 217, 195-202 (2010)]. Some examples are given to illustrate our obtained results. An application to the study of existence of solutions for a system of non-linear integral equations is also considered.

Common coupled fixed point theorems in cone metric spaces for w-compatible mappings

“…Abbas et al [1] introduced the concept of w-compatible mappings and obtained coupled coincidence point and coupled point of coincidence for mappings satisfying a contractive condition in cone metric spaces. Very recently, Aydi et al [11] introduced the concepts of wcompatible mappings and generalized the results in [1].…”

Coupled common fixed point theorems in partially ordered G-metric spaces for nonlinear contractions

“…Continuing this process, we can construct two sequences {x n } and {y n } in X such that (2) g(x n+1 ) = F (x n , y n ) and g(y n+1 ) = F (y n , x n ) ∀ n ≥ 0.…”

“…References [7,15,16] are some examples of these works. Now-a-days authors have keen interest in proving fixed point theorems in partially ordered metric spaces subjected to nonlinear contractive conditions, see [2,4,10,[18][19][20]. Our paper deals with the establishment of some coupled coincidence and Definition 1.3 ( [5]).…”

On mixed g-monotone and w-compatible mappings in ordered cone b-metric spaces

“…X. In subsequent papers several authors proved various coupled and common coupled fixed point theorems (e.g., [5][6][7][8][9][10][11][12][13][14]). …”