On Certain Reversed Mean Lipschitzian Mappings in Banach Spaces. (3rd October 2021)

• Record Type: Journal Article
• Authors: Bashir, Shahid; Malik, Muhammad Aslam; Husnine, Syed Muhammad
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 13(2021)
• Page Start: 1539
• Page End: 1554
• Publication Date: 2021-10-03
• Subjects: Fixed point property -- Mean Lipschitz constant -- Mean Lipschitzian mappings -- Reverse mean Lipschitz constant -- Reversed mean Lipschitzian mappings; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.2001748
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: We introduce reversed mean Lipschitzian mappings and find the bound for reversed mean Lipschitz constants of its iterates under certain conditions. Moreover, we prove that if a bounded closed and convex subset C of Banach space has fixed point property for nonexpansive mappings, then C also has fixed point property for certain reversed ( ( α, β ), 1 ) -Lipschitzian mappings such that α ≥ β .