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A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations. (English) Zbl 1197.54054

Let \((X,\leq)\) be a partially ordered set and \(d\) a complete metric on \(X\). The authors present a fixed point theorem for an operator \(f:X\to X\) under some suitable conditions in terms of \(\leq\) and \(d\). An application to ordinary differential equations is also given.

MSC:

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

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