Strong Convergence Theorems for Quasi-Nonexpansive Mappings and Uniformly L-Lipschitzian Asymptotically Pseudo-Contractive Mappings in Banach Spaces. (12th March 2018)

• Record Type: Journal Article
• Authors: Pathak, Hemant Kumar; Sahu, Vinod Kumar
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 4(2018)
• Page Start: 449
• Page End: 466
• Publication Date: 2018-03-12
• Subjects: Asymptotically nonexpansive mapping -- asymptotically pseudocontractive mapping -- fixed point -- normalized duality mapping -- quasi-nonexpansive mapping -- uniformly L-Lipschitzian -- weak uniformly L-Lipschitzian mapping; 47H09 -- 47H10 -- 47J25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1377228
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: A new 𝒮 -generated Ishikawa iteration with errors is proposed for a pair of quasi-nonexpansive mapping and uniformly L -Lipschitzian asymptotically pseudo-contractive mapping in real Banach spaces. We show that the proposed iterative scheme converges strongly to a common solution of quasi-nonexpansive mapping and uniformly L -Lipschitzian asymptotically pseudo-contractive mapping in real Banach spaces. A comparison table is prepared using a numeric example which shows that the proposed iterative algorithm is faster than some known iterative algorithms.