Approximating Fixed Points of Generalized α-Nonexpansive Mappings in Banach Spaces. (1st February 2017)

• Record Type: Journal Article
• Authors: Pant, Rajendra; Shukla, Rahul
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 2(2017)
• Page Start: 248
• Page End: 266
• Publication Date: 2017-02-01
• Subjects: Condition (C) -- generalized α-nonexpansive mapping -- α-nonexpansive mapping -- nonexpansive mapping -- Opial property; Primary: 47H10 -- 54H25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1276075
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: We introduce a new type of nonexpansive mappings and obtain a number of existence and convergence theorems. This new class of nonlinear mapping properly contains nonexpansive, Suzuki-type generalized nonexpansive mappings and partially extends firmly nonexpansive and α -nonexpansive mappings. Also, this class of mapping need not be continuous. Some useful examples are presented to illustrate facts. Some prominent iteration processes are also compared using numerical computations.