Existence and Iterative Approximation of Hybrid Best Proximity Points for Set-Valued Mappings*. (11th June 2021)

• Record Type: Journal Article
• Authors: Hong, Shihuang; Shao, Menghao; Luo, Xinggang
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 8(2021)
• Page Start: 883
• Page End: 901
• Publication Date: 2021-06-11
• Subjects: Hybrid best proximity point -- partially ordered set -- proximally mixed monotone mapping -- proximally ordered contraction; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1933520
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, hybrid best proximity points for a class of proximally mixed monotone set-valued mappings are discussed. In order to get rid of the fetter of continuity, we introduce the proximally ordered contraction instead of various proximal distance contractions widely applied in recent literatures and present some new existence and iterative approximation theorems of best proximity points for such mappings. Some examples are given to illustrate the advantages of the obtained results.