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Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. (English) Zbl 1176.54032
The authors introduce the concept of a g-monotone mapping and prove coupled coincidence and coupled common fixed point theorems for such nonlinear contractive mappings in partially ordered complete metric spaces. The presented theorems are generalizations of the recent fixed point theorems due to T. G. Bhaskar and V. Lakshmikantham [Nonlinear Anal., Theory Methods Appl. 65, No. 7 (A), 1379–1393 (2006; Zbl 1106.47047)] and include several recent developments.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
47H10 Fixed-point theorems
34B15 Nonlinear boundary value problems for ordinary differential equations
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