Abstract
Abstract In this paper, employing a new concept of generalized compatibility of a pair of mappings defined on a product space, certain coupled coincidence point results of mappings involved herein are obtained. We also deduce certain coupled fixed point results without mixed monotone property of F. Our results generalize some recent comparable results in the literature. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results. MSC:46S40, 47H10, 54H25.
Highlights
1 Introduction The existence of fixed points in ordered metric spaces has been investigated by Ran and Reurings [ ]
The study of coupled fixed points in partially ordered metric spaces was initiated by Guo and Lakshmikantham [ ], and attracted many researchers, see for example [ – ] and references therein
Assume that F, G : X × X → X are two generalized compatible mappings such that F is G-increasing with respect to, G is continuous and has the mixed monotone property, and there exist two elements x, y ∈ X with
Summary
The existence of fixed points in ordered metric spaces has been investigated by Ran and Reurings [ ]. Assume that F, G : X × X → X are two generalized compatible mappings such that F is G-increasing with respect to , G is continuous and has the mixed monotone property, and there exist two elements x , y ∈ X with
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