Diametrically Regular Mappings and Browder's Theorem Without the Endpoint Condition. (11th March 2020)

• Record Type: Journal Article
• Authors: Panyanak, B.; Suantai, S.
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 4(2020)
• Page Start: 495
• Page End: 505
• Publication Date: 2020-03-11
• Subjects: Browder's theorem -- diametrically regular mapping -- endpoint -- fixed point -- nonexpansive mapping; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1680562
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we introduce the class of diametrically regular mappings and prove that it includes the class of multi-valued mappings having endpoints. We also prove the existence of endpoints and the convergence of an iterative process for mappings of this class. Our approach provides a new idea of proving Browder's theorem without the endpoint condition.