Best Proximity Point Results for Geraghty Type Ƶ-Proximal Contractions with an Application
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Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam
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Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam
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Institut Supérieur d’Informatique et des Techniques de Communication, Université de Sousse, H. Sousse 4000, Tunisia
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Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
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Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
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Author to whom correspondence should be addressed.
Axioms 2019, 8(3), 81; https://doi.org/10.3390/axioms8030081
Received: 18 June 2019 / Revised: 10 July 2019 / Accepted: 11 July 2019 / Published: 18 July 2019
(This article belongs to the Special Issue Fixed Point Theory and Related Topics)
In this study, we establish the existence and uniqueness theorems of the best proximity points for Geraghty type Ƶ-proximal contractions defined on a complete metric space. The presented results improve and generalize some recent results in the literature. An example, as well as an application to a variational inequality problem are also given in order to illustrate the effectiveness of our generalizations.
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Keywords:
best proximity point; Ƶ-contraction; geraghty type contraction; simulation function; admissible mapping; variational inequality
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
MDPI and ACS Style
Işık, H.; Aydi, H.; Mlaiki, N.; Radenović, S. Best Proximity Point Results for Geraghty Type Ƶ-Proximal Contractions with an Application. Axioms 2019, 8, 81.
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