Abstract
In this paper coupled coincidence points of mappings satisfying a nonlinear contractive condition in the framework of partially ordered metric spaces are obtained. Our results extend the results of Harjani et al. (2011). Moreover, an example of the main result is given. Finally, some coupled coincidence point results for mappings satisfying some contraction conditions of integral type in partially ordered complete metric spaces are deduced.
Highlights
Introduction and Mathematical PreliminariesThe existence of fixed points for certain mappings in ordered metric spaces has been studied and applied by Ran and Reurings 1 and by Nieto and Rodrıguez-Lopez 2
Many researchers have obtained fixed point and common fixed point results for mappings under various contractive conditions in different metric spaces see, e.g., 3–8
Existence of coupled fixed points in partially ordered metric spaces was first investigated in 2006 by Bhaskar and Lakshmikantham 9 and by Lakshmikantham and Ciric 10. Further results in this direction under weak contraction conditions in different metric spaces were proved in, for example, 4, 5, 10–15
Summary
The existence of fixed points for certain mappings in ordered metric spaces has been studied and applied by Ran and Reurings 1 and by Nieto and Rodrıguez-Lopez 2. Many researchers have obtained fixed point and common fixed point results for mappings under various contractive conditions in different metric spaces see, e.g., 3–8. Existence of coupled fixed points in partially ordered metric spaces was first investigated in 2006 by Bhaskar and Lakshmikantham 9 and by Lakshmikantham and Ciric 10. Further results in this direction under weak contraction conditions in different metric spaces were proved in, for example, 4, 5, 10–15. One can say that F has the mixed monotone property if F x, y is monotone nondecreasing in x and is monotone nonincreasing in y, that is, for all x1, x2 ∈ X, x1 x2 implies F x1, y F x2, y for any y ∈ X, and for all y1, y2 ∈ X, y1 y2 implies F x, y1 F x, y2 for any x ∈ X
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