Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 1, Number 2 (2010), 46-56 .
Coupled fixed point, $F$-invariant set and fixed point of $N$-order
Bessem Samet and Calogero Vetro
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.
Article information
Source
Ann. Funct. Anal., Volume 1, Number 2 (2010), 46-56 .
Dates
First available in Project Euclid: 12 May 2014
Permanent link to this document
https://projecteuclid.org/euclid.afa/1399900586
Digital Object Identifier
doi:10.15352/afa/1399900586
Mathematical Reviews number (MathSciNet)
MR2772037
Zentralblatt MATH identifier
1214.54041
Subjects
Primary: 54H25: Fixed-point and coincidence theorems [See also 47H10, 55M20]
Secondary: 47H10 34B15
Keywords
Coupled fixed point $F$-invariant set fixed point of $N$-order partially ordered set cone metric space
Citation
Samet, Bessem; Vetro, Calogero. Coupled fixed point, $F$-invariant set and fixed point of $N$-order. Ann. Funct. Anal. 1 (2010), no. 2, 46--56. doi:10.15352/afa/1399900586. https://projecteuclid.org/euclid.afa/1399900586