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Coupled fixed point theorems for mixed monotone mappings and an application to integral equations. (English) Zbl 1236.47056
Summary: We extend the coupled fixed point theorems for a mixed monotone mapping F:X×XX in partially ordered metric spaces established by T. G. Bhaskar and V. Lakshmikantham [Nonlinear Anal., Theory Methods Appl. 65, No. 7, 1379–1393 (2006; Zbl 1106.47047)]. An application to nonlinear integral equations is also given to illustrate our results.
MSC:
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47H07Monotone and positive operators on ordered topological linear spaces
54F05Linearly, generalized, and partial ordered topological spaces
54E40Special maps on metric spaces
54H25Fixed-point and coincidence theorems in topological spaces
47N20Applications of operator theory to differential and integral equations
References:
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