Coupled fixed point theorems in cone metric spaces with a c-distance and applications

*Correspondence: [email protected]; [email protected] 2Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, 10140, Thailand Full list of author information is available at the end of the article Abstract In this paper, we extend the very recent result of Sintunavarat et al. in the paper ‘Coupled fixed point theorems for weak contraction mapping under F-invariant set’ (Abstr. Appl. Anal. 2012:324874, 2012). In particular, we give an example of a nonlinear contraction mapping for which our result successfully detects a coupled fixed point in contrast to the result of Sintunavarat et al., which is not applied to show the existence of a coupled fixed point. As a consequence, the main results in this paper extend and unify many results in the topic of coupled fixed points including the results of Sintunavarat et al. Also, some applications of the main results are given. MSC: 54H25; 47H10