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Zbl 1214.54041
Samet, B.; Vetro, C.
Coupled fixed point, $F$-invariant set and fixed point of $N$-order. (English)
[J] Ann. Funct. Anal. AFA 1, No. 2, 46-56, electronic only (2010). ISSN 2008-8752/e

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 2000:: *54H25 Fixed-point theorems in topological spaces
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
34B15 Nonlinear boundary value problems of ODE

Keywords: coupled fixed point; $F$-invariant set; fixed point of $N$-order; partially ordered set; cone metric space

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Zentralblatt MATH Berlin [Germany]