Convergence and Best Proximity Points for Generalized Contraction Pairs

Slah Sahmim, Abdelbasset Felhi and Hassen Aydi
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Slah Sahmim: Department of Mathematics and Statistics, College of Sciences, King Faisal University, P.O. Box 400, Hafouf 31982, Saudi Arabia
Abdelbasset Felhi: Department of Mathematics and Physics Preparatory Engineering Institute, Carthage University, Bizerte 7021, Tunisia
Hassen Aydi: Department of Mathematics, College of Education of Jubail, Imam Abdulrahman Bin Faisal University, P.O. 12020, Industrial Jubail 31961, Saudi Arabia

Mathematics, 2019, vol. 7, issue 2, 1-12

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.

Keywords: contraction pair; proximally-complete pair; semi-sharp proximinal; best proximity point; nonexpansive mapping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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