Existence of Best Proximity Pairs and a Generalization of Carathéodory Theorem. (8th December 2020)

• Record Type: Journal Article
• Authors: Digar, Abhik; Kosuru, G. Sankara Raju
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 15(2020)
• Page Start: 1901
• Page End: 1911
• Publication Date: 2020-12-08
• Subjects: Best approximate solution -- best proximity pair -- Carathéodory extension theorem -- initial value problem -- relatively continuous mapping; 47H10 -- 47H04 -- 35F25 -- 47N20; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1859529
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: A new class of mappings, called relatively continuous, is introduced and incorporated to elicit best proximity pair theorems for a non-self-mapping in the setting of reflexive Banach space. As a consequence we obtain a generalization of Carathéodory extension theorem for an initial value problem with L 1 functions on the right hand side.