Coupled common fixed point results in ordered \(S\)-metric spaces (Q326876)

Summary: The notion of coupled fixed point theorem introduced by \textit{T. G. Bhaskar} and \textit{V. Lakshmikantham} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 65, No. 7, 1379--1393 (2006; Zbl 1106.47047)] and \textit{S. Sedghi} et al. [Mat. Vesn. 64, No. 3, 258--266 (2012; Zbl 1289.54158)] introduced the concept of \(S\)-metric space. Our aim of this article is to extend the concept of coupled fixed point in \(S\)-metric space and prove a coupled coincidence and common fixed point theorems for commuting mappings with mixed \(g\)-monotone property in partially ordered \(S\)-metric spaces. We also give some examples in support of our theorem.