Annals of Functional Analysis

Coupled fixed point‎, ‎$F$-invariant set and fixed point of $N$-order

Bessem Samet and Calogero Vetro

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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


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