Next Article in Journal
Monte Carlo Algorithms for the Parabolic Cauchy Problem
Next Article in Special Issue
Extension and Application of the Yamada Iteration Algorithm in Hilbert Spaces
Previous Article in Journal
Cumulative Measure of Inaccuracy and Mutual Information in k-th Lower Record Values
Previous Article in Special Issue
Convergence Theorems for Modified Inertial Viscosity Splitting Methods in Banach Spaces
Article

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

Sahmim, S.; Felhi, A.; Aydi, H. Convergence and Best Proximity Points for Generalized Contraction Pairs. Mathematics 2019, 7, 176. https://doi.org/10.3390/math7020176

AMA Style

Sahmim S, Felhi A, Aydi H. Convergence and Best Proximity Points for Generalized Contraction Pairs. Mathematics. 2019; 7(2):176. https://doi.org/10.3390/math7020176

Chicago/Turabian Style

Sahmim, Slah, Abdelbasset Felhi, and Hassen Aydi. 2019. "Convergence and Best Proximity Points for Generalized Contraction Pairs" Mathematics 7, no. 2: 176. https://doi.org/10.3390/math7020176

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop