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Fixed point theorems for mixed monotone operators and applications to integral equations. (English) Zbl 1218.54040
The authors generalize Theorem 1 of [T. G. Bhaskar and V. Lakshmikantham, Nonlinear Anal., Theory Methods Appl. 65, No. 7, A, 1379–1393 (2006; Zbl 1106.47047)] by using altering distance functions and present some coupled fixed point theorems for a mixed monotone operator in a complete metric space endowed with a partial order. They also provide an application to integral equations.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
54E50 Complete metric spaces
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
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