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Fixed point theorems for generalized contractions in partially ordered metric spaces with semi-monotone metric. (English) Zbl 1221.54072
The author studies the existence and uniqueness of fixed points for mixed monotone mappings in a partially ordered metric space with a semi-monotone metric, and obtains the existence and uniqueness of the solution to a periodic boundary value problem for a first-order differential equation with periodic boundary conditions as an application.

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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