A hybrid method for solving variational inequalities over the common fixed point sets of infinite families of nonexpansive mappings in Banach spaces. (1st September 2020)

• Record Type: Journal Article
• Authors: Nguyen, Thi Thu Thuy; Pham, Thanh Hieu
• Is Part Of: Optimization. Volume 69:Number 9(2020)
• Page Start: 2155
• Page End: 2176
• Publication Date: 2020-09-01
• Subjects: Accretive mappings -- fixed points -- nonexpansive mappings -- hybrid method -- variational inequalities; 41A65 -- 47H17 -- 47H20; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1647201
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we introduce a hybrid method, a combination of the steepest-descent method and the Krasnosel'skii-Mann one, for solving a variational inequality over the set of common fixed points of an infinite family of nonexpansive mappings in Banach spaces under two different conditions on the Banach space, either a uniformly smooth Banach space or a reflexive and strictly convex one with a uniformly Gâteaux differentiable norm, without imposing the sequential weak continuity of the normalized duality mapping. The method is an improvement and extension of some other published results. We also give a numerical example to illustrate the convergence analysis of the proposed method.