Two extensions of coupled coincidence point results for nonlinear contractive mappings
Inspired by the notion of coupled coincidence point results due to \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{V. Lakshmikantham} and \textit{L. Ćirić} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 12, 4341--4349 (2009; Zbl 1176.54032)], the authors introduce the concept of a mixed fg-monotone mapping and prove a coupled coincidence fixed point theorem (Theorem 2.4) for nonlinear contractive mappings in partially ordered complete metric spaces. The proof of the theorem is valid under the assumed conditions. A~suitable example (Example 2.5) is also given to support Theorem 2.4. One more interesting result is proved in the framework of partially ordered probabilistic metric spaces, which extends the results of \textit{L. Ćirić} et al. [Fixed Point Theory Appl. 2011, Article ID 56, 13 p. (2011; Zbl 1271.54078)] to a more general class of \(t\)-norms mentioned in Example 1.7.
scientific article; zbMATH DE number 6513990
scientific article