Self-Adaptive Extragradient Methods for Solving Variational Inequalities and Fixed Point Problems in 2-Uniformly Convex and Uniformly Smooth Banach Spaces. (26th August 2022)

• Record Type: Journal Article
• Authors: Hu, Shaotao; Wang, Yuanheng; Dong, Qiao-Li
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 12(2022)
• Page Start: 1401
• Page End: 1422
• Publication Date: 2022-08-26
• Subjects: Extragradient method -- Variational inequality -- Pseudomonotone operator -- Strong convergence -- Fixed point -- 2-uniformly convex Banach spaces; 47H05 -- 47J25 -- 47H10 -- 65J15 -- 65K15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2108834
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we mainly introduce a new and different self adaptive extragradient algorithm with an inertial technique for solving variational inequality problems of pseudomonotone operators and fixed point problems of relatively nonexpansive mappings in 2-uniformly convex and uniformly smooth Banach spaces. Under some appropriate assumptions imposed on the parameters and operators, we prove that the iterative sequence generated by our proposed algorithm converges strongly to a common solution of variational inequality problems and fixed point problems. Moreover, we give some numerical examples to show the effectiveness and feasibility of our algorithm.