Local Uniform Strong Proximinality of the Space of Continuous Vector-Valued Functions. (3rd August 2017)

• Record Type: Journal Article
• Authors: Indumathi, V.; Prakash, N.
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 8(2017)
• Page Start: 1014
• Page End: 1023
• Publication Date: 2017-08-03
• Subjects: 1 ½-ball property -- Hausdorff metric continuous -- metric projection -- proximinal -- strongly proximinal -- U-proximinal; 46B20 -- 41A50 -- 41A65; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1296863
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: Let X be a Banach space, S be a compact Hausdorff space and Y be a U-proximinal subspace of X . We prove that C ( S, Y ) is locally uniformly strongly proximinal in C ( S, X ) and the corresponding metric projection map is Hausdorff metric continuous.