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Coupled fixed point, $$F$$-invariant set and fixed point of $$N$$-order. (English) Zbl 1214.54041
Summary: In this paper, we establish some new coupled fixed point theorems in complete metric spaces, using a new concept of $$F$$-invariant set. We introduce the notion of fixed point of $$N$$-order as natural extension of that of coupled fixed point. As applications, we discuss and adapt the presented results to the setting of partially ordered cone metric spaces. The presented results extend and complement some known existence results from the literature.

MSC:
 54H25 Fixed-point and coincidence theorems (topological aspects) 47H10 Fixed-point theorems 34B15 Nonlinear boundary value problems for ordinary differential equations
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