Communications in Mathematical Analysis

Fixed Point Theorems on a Metric Space Endowed With an Arbitrary Binary Relation and Applications

B. Samet and M. Turinici

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Abstract

In this paper, we establish fixed point theorems for contractive mappings on a metric space endowed with an amorphous binary relation. The presented theorems extend and generalize many existing results on metric and ordered metric spaces. We apply also our main result to derive fixed point theorems for cyclical contractive mappings.

Article information

Source
Commun. Math. Anal., Volume 13, Number 2 (2012), 82-97.

Dates
First available in Project Euclid: 9 October 2012

Permanent link to this document
https://projecteuclid.org/euclid.cma/1349803595

Mathematical Reviews number (MathSciNet)
MR2998356

Zentralblatt MATH identifier
1259.54024

Subjects
Primary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 54H25: Fixed-point and coincidence theorems [See also 47H10, 55M20]

Keywords
Fixed point metric space binary relation ordered set cyclical mappings

Citation

Samet, B.; Turinici, M. Fixed Point Theorems on a Metric Space Endowed With an Arbitrary Binary Relation and Applications. Commun. Math. Anal. 13 (2012), no. 2, 82--97. https://projecteuclid.org/euclid.cma/1349803595


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