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.
Samet, B., Vetro, C. (2010). Coupled fixed point, F-invariant set and fixed point of N-order. ANNALS OF FUNCTIONAL ANALYSIS, 1(2), 46-56.
Coupled fixed point, F-invariant set and fixed point of N-order
VETRO, Calogero
2010-01-01
Abstract
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.
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