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Zbl 1230.54047
Shatanawi, W.
Coupled fixed point theorems in generalized metric spaces. (English)
[J] Hacet. J. Math. Stat. 40, No. 3, 441-447 (2011). ISSN 1303-5010

Summary: {\it T. G. Bhaskar} and {\it V. Lakshmikantham} [Nonlinear Anal., Theory Methods Appl. 65, No.~7, 1379--1393 (2006; Zbl 1106.47047)] and {\it V. Lakshmikantham} and {\it Lj. B. Ćirić} [ibid. 70, No.~12, A, 4341--4349 (2009; Zbl 1176.54032)] introduced the concept of a coupled coincidence point of a mapping $F$ from $X\times X$ into $X$ and a mapping $g$ from $X$ into $X$. In the present paper, we prove a coupled coincidence fixed point theorem in the setting of a generalized metric space in the sense of Z. Mustafa and B. Sims.

MSC 2000:: *54H25 Fixed-point theorems in topological spaces
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
54E50 Complete metric spaces

Keywords: common fixed point; coupled coincidence fixed point; generalized metric space

Citations: Zbl 1106.47047; Zbl 1176.54032

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