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Mathematics 2019, 7(2), 176; https://doi.org/10.3390/math7020176

Convergence and Best Proximity Points for Generalized Contraction Pairs

1
Department of Mathematics and Statistics, College of Sciences, King Faisal University, P.O. Box 400, Hafouf 31982, Saudi Arabia
2
Department of Mathematics and Physics Preparatory Engineering Institute, Carthage University, Bizerte 7021, Tunisia
3
Department of Mathematics, College of Education of Jubail, Imam Abdulrahman Bin Faisal University, P.O. 12020, Industrial Jubail 31961, Saudi Arabia
*
Author to whom correspondence should be addressed.
Received: 12 December 2018 / Revised: 7 February 2019 / Accepted: 8 February 2019 / Published: 15 February 2019
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)
Full-Text   |   PDF [253 KB, uploaded 15 February 2019]

Abstract

This paper is devoted to studying the existence of best proximity points and convergence for a class of generalized contraction pairs by using the concept of proximally-complete pairs and proximally-complete semi-sharp proximinal pairs. The obtained results are generalizations of the result of Sadiq Basha (Basha, S., Best proximity points: global optimal approximate solutions, J. Glob. Optim. 2011, 49, 15–21) As an application, we give a result for nonexpansive mappings in normed vector spaces. View Full-Text
Keywords: contraction pair; proximally-complete pair; semi-sharp proximinal; best proximity point; nonexpansive mapping contraction pair; proximally-complete pair; semi-sharp proximinal; best proximity point; nonexpansive mapping
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 (CC BY 4.0).
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Sahmim, S.; Felhi, A.; Aydi, H. Convergence and Best Proximity Points for Generalized Contraction Pairs. Mathematics 2019, 7, 176.

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