Generalized coupled common fixed point results in partially ordered A-metric spaces

Mujahid Abbas; Bashir Ali; Yusuf I. Suleiman

doi:10.1186/s13663-015-0309-2

Generalized coupled common fixed point results in partially ordered A-metric spaces

Mujahid Abbas
, Bashir Ali
, Yusuf I. Suleiman

Research output: Contribution to journal › Article › peer-review

47 Citations (Scopus)

Abstract

Sedghi et al. (Mat. Vesn. 64(3):258-266, 2012) introduced the notion of a S-metric as a generalized metric in 3-tuples S:X³→[0,∞), where X is a nonempty set. The aim of this paper is to introduce the concept of an n-tuple metric A:Xⁿ→[0,∞) and to study its basic topological properties. We also prove some generalized coupled common fixed point theorems for mixed weakly monotone maps in partially ordered A-metric spaces. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.

Original language	English
Pages (from-to)	1-24
Number of pages	24
Journal	Fixed Point Theory and Algorithms for Sciences and Engineering
Volume	2015
Issue number	1
DOIs	https://doi.org/10.1186/s13663-015-0309-2
Publication status	Published - 1 Dec 2015
Externally published	Yes

Keywords

2-metric spaces
A-metric spaces
D-metric spaces
D∗-metric spaces
G-metric spaces
S-metric spaces
coupled common fixed point
mixed weakly monotone maps

ASJC Scopus subject areas

Geometry and Topology
Applied Mathematics

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10.1186/s13663-015-0309-2

Cite this

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title = "Generalized coupled common fixed point results in partially ordered A-metric spaces",

abstract = "Sedghi et al. (Mat. Vesn. 64(3):258-266, 2012) introduced the notion of a S-metric as a generalized metric in 3-tuples S:X3→[0,∞), where X is a nonempty set. The aim of this paper is to introduce the concept of an n-tuple metric A:Xn→[0,∞) and to study its basic topological properties. We also prove some generalized coupled common fixed point theorems for mixed weakly monotone maps in partially ordered A-metric spaces. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.",

keywords = "2-metric spaces, A-metric spaces, D-metric spaces, D∗-metric spaces, G-metric spaces, S-metric spaces, coupled common fixed point, mixed weakly monotone maps",

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doi = "10.1186/s13663-015-0309-2",

language = "English",

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T1 - Generalized coupled common fixed point results in partially ordered A-metric spaces

AU - Abbas, Mujahid

AU - Ali, Bashir

AU - Suleiman, Yusuf I.

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Y1 - 2015/12/1

N2 - Sedghi et al. (Mat. Vesn. 64(3):258-266, 2012) introduced the notion of a S-metric as a generalized metric in 3-tuples S:X3→[0,∞), where X is a nonempty set. The aim of this paper is to introduce the concept of an n-tuple metric A:Xn→[0,∞) and to study its basic topological properties. We also prove some generalized coupled common fixed point theorems for mixed weakly monotone maps in partially ordered A-metric spaces. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.

AB - Sedghi et al. (Mat. Vesn. 64(3):258-266, 2012) introduced the notion of a S-metric as a generalized metric in 3-tuples S:X3→[0,∞), where X is a nonempty set. The aim of this paper is to introduce the concept of an n-tuple metric A:Xn→[0,∞) and to study its basic topological properties. We also prove some generalized coupled common fixed point theorems for mixed weakly monotone maps in partially ordered A-metric spaces. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.

KW - 2-metric spaces

KW - A-metric spaces

KW - D-metric spaces

KW - D∗-metric spaces

KW - G-metric spaces

KW - S-metric spaces

KW - coupled common fixed point

KW - mixed weakly monotone maps

UR - https://www.scopus.com/pages/publications/84928889441

U2 - 10.1186/s13663-015-0309-2

DO - 10.1186/s13663-015-0309-2

M3 - Article

AN - SCOPUS:84928889441

SN - 1687-1820

VL - 2015

SP - 1

EP - 24

JO - Fixed Point Theory and Algorithms for Sciences and Engineering

JF - Fixed Point Theory and Algorithms for Sciences and Engineering

IS - 1

ER -

Generalized coupled common fixed point results in partially ordered A-metric spaces

Abstract

Keywords

ASJC Scopus subject areas

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