On Bregman Best Proximity Points in Banach Spaces. (3rd April 2017)

• Record Type: Journal Article
• Authors: Naraghirad, Eskandar
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 4(2017)
• Page Start: 409
• Page End: 426
• Publication Date: 2017-04-03
• Subjects: Bregman best proximity point -- Bregman cyclic contraction mapping -- Bregman distance -- Bregman function -- Bregman sharp proximal pair; 47H10 -- 37C25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1251454
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, using Bregman functions and Bregman distances, we first introduce the notion of Bregman best proximity points, extending the notion of best proximity points introduced and studied in [1 ]. We then prove existence and convergence results of Bregman best proximity points for Bregman cyclic contraction mappings in the setting of Banach spaces. It is well known that the Bregman distance does not satisfy either the symmetry property or the triangle inequality which are required for standard distances. Numerical examples are included at the end of the paper. So, our results improve and generalize many known results in the current literature.