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Reseach Article
Best Proximity Point for Generalized Geraghty-Contractions with MT-Condition
| 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
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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