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Fixed point theorems in partially ordered metric spaces and applications. (English) Zbl 1106.47047
This paper gives some coupled fixed point theorems for a monotone mapping in a metric space endowed with a partial order, using a weak contractivity type assumption. Besides including several recent developments, the theorems can be used to investigate a class of problems. As an application, the existence and uniqueness of solutions for a periodic boundary value problem are discussed.

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