Coupled fixed-point theorems for contractions in partially ordered metric spaces and applications (Q1954475)

Summary: \textit{T. G. Bhaskar} and \textit{V. Lakshmikantham} [Nonlinear Anal., Theory Methods Appl. 65, No. 7, A, 1379--1393 (2006; Zbl 1106.47047)] showed the existence of coupled coincidence points of a mapping \(F\) from \(X \times X\) into \(X\) and a mapping \(g\) from \(X\) into \(X\) with some applications. The aim of this paper is to extend the results of Bhaskar and Lakshmikantham and improve the recent fixed-point theorems due to \textit{B. Samet} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 12, 4508--4517 (2010; Zbl 1264.54068)]. Indeed, we introduce the definition of generalized \(g\)-Meir-Keeler type contractions and prove some coupled fixed point theorems under a generalized \(g\)-Meir-Keeler-contractive condition. Also, some applications of the main results in this paper are given.