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Coupled fixed points in partially ordered metric spaces and application. (English) Zbl 1202.54036

Summary: We prove some coupled fixed point theorems for mappings having a mixed monotone property in partially ordered metric spaces. The main results of this paper are generalizations of the main results of T.G.Bhaskar and V.Lakshmikantham [Nonlinear Anal., Theory Methods Appl.65, No.7 (A), 1379–1393 (2006; Zbl 1106.47047)]. As an application, we discuss the existence and uniqueness for a solution of a nonlinear integral equation.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
45G10 Other nonlinear integral equations

Citations:

Zbl 1106.47047
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References:

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