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Volume 2020

The existence and uniqueness of $\varphi-$Best proximity point theorems for generalized Boyd-Wong proximal contraction -by Urairat Deepan and Poom Kumam

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Abstract: In this paper, we study concept and expand the condition of I\c{s}ik, Sezen and Vetro [1] to prove the existence and uniqueness of $\varphi-$best proximity point for $(F,\lambda,\varphi)-$weak proximal and $(F,\lambda,\varphi)-$proximal contraction. As for applications of our main results, we prove the existence and uniqueness of a fixed point on partial metric spaces and variational inequality.

Keywords: $(F,\lambda, \varphi)-$proximal contraction, $(F,\lambda,\varphi)-$weak proximal contraction, $\varphi-$best proximity point, partial metric space.

DOI: 10.30697/rfpta-2019-026

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How to cite this article: Urairat Deepan and Poom Kumam, The existence and uniqueness of $\varphi-$Best proximity point theorems for generalized Boyd-Wong proximal contraction, Res. Fixed Point Theory Appl.,Volume 2020, Article ID 2019026, 13 pages, 2020. DOI: https://doi.org/10.30697/rfpta-2019-026

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Copyright © 2020 SUMA Publishing Group., This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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