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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 $\left(X,\le \right)$ 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 $\le$ and $d$. An application to ordinary differential equations is also given.

##### MSC:
 54H25 Fixed-point and coincidence theorems in topological spaces 54F05 Linearly, generalized, and partial ordered topological spaces 34B15 Nonlinear boundary value problems for ODE