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

Nguyen Van Luong; Nguyen Xuan Thuan

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 3, 983-992 (2011).

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

Keywords:

coupled fixed point; mixed monotone mapping; partially ordered set; nonlinear integral equation; existence and uniqueness of a solution

Citations:

Zbl 1106.47047

References:

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