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Partially ordered cone metric spaces and coupled fixed point results. (English) Zbl 1205.54044
Summary: {\it T. G. Bhaskar} and {\it V. Lakshmikantham} [Nonlinear Anal., Theory Methods Appl. 65, No. 7 (A), 1379--1393 (2006; Zbl 1106.47047)] studied the coupled coincidence point of a mapping $F$ from $X\times X$ into $X$ and a mapping $g$ from $X$ into $X$. {\it E. Karapinar} [Comput. Math. Appl. 59, No. 12, 3656--3668 (2010; Zbl 1198.65097)] proved some results of the coupled coincidence point of a mapping $F$ from $X\times X$ into $X$ and a mapping $g$ from $X$ into $X$ over normal cones without regularity. In the present paper, we prove that coupled coincidence fixed point theorems over cone metric spaces are not necessarily normal. Our results generalize several well known comparable results in the literature.

##### MSC:
 54H25 Fixed-point and coincidence theorems in topological spaces 47H10 Fixed-point theorems for nonlinear operators on topological linear spaces
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##### References:
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