A graphical version of Reich’s fixed point theorem

Monther R. Alfuraidan; Mostafa Bachar; Mohamed A. Khamsi

doi:10.22436/jnsa.009.06.40

A graphical version of Reich’s fixed point theorem

Monther R. Alfuraidan, Mostafa Bachar, Mohamed A. Khamsi

Mathematics

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

6 Scopus citations

Abstract

In this paper, we discuss the definition of the Reich multivalued monotone contraction mappings defined in a metric space endowed with a graph. In our investigation, we prove the existence of fixed point results for these mappings. We also introduce a vector valued Bernstein operator on the space C([0, 1],X), where X is a Banach space endowed with a partial order. Then we give an analogue to the Kelisky-Rivlin theorem.

Original language	British English
Pages (from-to)	3931-3938
Number of pages	8
Journal	Journal of Nonlinear Science and Applications
Volume	9
Issue number	6
DOIs	https://doi.org/10.22436/jnsa.009.06.40
State	Published - 2016

Keywords

Fixed point theory
Graph theory
Multivalued monotone contraction
Partial order

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10.22436/jnsa.009.06.40

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abstract = "In this paper, we discuss the definition of the Reich multivalued monotone contraction mappings defined in a metric space endowed with a graph. In our investigation, we prove the existence of fixed point results for these mappings. We also introduce a vector valued Bernstein operator on the space C([0, 1],X), where X is a Banach space endowed with a partial order. Then we give an analogue to the Kelisky-Rivlin theorem.",

keywords = "Fixed point theory, Graph theory, Multivalued monotone contraction, Partial order",

author = "Alfuraidan, {Monther R.} and Mostafa Bachar and Khamsi, {Mohamed A.}",

note = "Funding Information: The authors would like to extend their sincere appreciation to the Deanship of Scientific Research at King Saud University for funding this Research group No. (RG-1435-079). Publisher Copyright: {\textcopyright} 2016 All rights reserved.",

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AU - Alfuraidan, Monther R.

AU - Bachar, Mostafa

AU - Khamsi, Mohamed A.

N1 - Funding Information: The authors would like to extend their sincere appreciation to the Deanship of Scientific Research at King Saud University for funding this Research group No. (RG-1435-079). Publisher Copyright: © 2016 All rights reserved.

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Y1 - 2016

N2 - In this paper, we discuss the definition of the Reich multivalued monotone contraction mappings defined in a metric space endowed with a graph. In our investigation, we prove the existence of fixed point results for these mappings. We also introduce a vector valued Bernstein operator on the space C([0, 1],X), where X is a Banach space endowed with a partial order. Then we give an analogue to the Kelisky-Rivlin theorem.

AB - In this paper, we discuss the definition of the Reich multivalued monotone contraction mappings defined in a metric space endowed with a graph. In our investigation, we prove the existence of fixed point results for these mappings. We also introduce a vector valued Bernstein operator on the space C([0, 1],X), where X is a Banach space endowed with a partial order. Then we give an analogue to the Kelisky-Rivlin theorem.

KW - Fixed point theory

KW - Graph theory

KW - Multivalued monotone contraction

KW - Partial order

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SP - 3931

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JO - Journal of Nonlinear Science and Applications

JF - Journal of Nonlinear Science and Applications

IS - 6

ER -

A graphical version of Reich’s fixed point theorem

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Keywords

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