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

By Hassen Aydi, Bessem Samet, Calogero Vetro. 2011

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In this paper, we introduce the concepts of -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 b-common 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.2010 Mathematics Subject Classifications: 54H25; 47H10.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c72d0c986bb3b720955080ab1566881c67155f28