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Best Proximity Point for Generalized Geraghty-Contractions with MT-Condition

by Savita Ratheee, Kusum Dhingra
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 127 - Number 8
Year of Publication: 2015
Authors: Savita Ratheee, Kusum Dhingra
10.5120/ijca2015906386

Savita Ratheee, Kusum Dhingra . Best Proximity Point for Generalized Geraghty-Contractions with MT-Condition. International Journal of Computer Applications. 127, 8 ( October 2015), 8-11. DOI=10.5120/ijca2015906386

@article{ 10.5120/ijca2015906386,
author = { Savita Ratheee, Kusum Dhingra },
title = { Best Proximity Point for Generalized Geraghty-Contractions with MT-Condition },
journal = { International Journal of Computer Applications },
issue_date = { October 2015 },
volume = { 127 },
number = { 8 },
month = { October },
year = { 2015 },
issn = { 0975-8887 },
pages = { 8-11 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume127/number8/22747-2015906386/ },
doi = { 10.5120/ijca2015906386 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T23:19:19.117264+05:30
%A Savita Ratheee
%A Kusum Dhingra
%T Best Proximity Point for Generalized Geraghty-Contractions with MT-Condition
%J International Journal of Computer Applications
%@ 0975-8887
%V 127
%N 8
%P 8-11
%D 2015
%I Foundation of Computer Science (FCS), NY, USA
Abstract

A best proximity point for a non-selfmapping is that point whose distance from its image is as small as possible. In mathematical language, if X is any space, A and B are two subsets of X and T: A → B is a mapping. We can say that x is best proximity point if d(x, Tx) = d(A, B) and this best proximity point reduces to fixed point if mapping T is a selfmapping. The main objective in this paper is to prove the best proximity point theorem for the notion of Geraghty-contractions by using MT-function β which satisfies Mizoguchi-Takahashi’s condition (equation (i)) in the context of metric space and we also provide an example to support our main result.

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Index Terms

Computer Science
Information Sciences

Keywords

Best proximity point P-property MT-condition.

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