Fixed point theorems in partially ordered metric spaces and applications. (English) Zbl 1106.47047

Bhaskar, T. Gnana; Lakshmikantham, V.

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 65, No. 7, 1379-1393 (2006).

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.

Reviewer: Zhang Xian (Xiamen)

MSC:

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

Keywords:

coupled fixed point; partially ordered set; coupled upper, lower solution; periodic boundary value problem

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