Strong Convergence of New Algorithm for Monotone Operator in Banach Spaces. (10th September 2019)

• Record Type: Journal Article
• Authors: Tang, Yan
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 12(2019)
• Page Start: 1426
• Page End: 1447
• Publication Date: 2019-09-10
• Subjects: Monotone mappings -- zero point -- equilibrium problem -- strong convergence -- approximating; 47H09 -- 47H10 -- 47L25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1606825
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: Let E be a uniformly convex and uniformly smooth real Banach space with dual E * . The convergence of a new iterative algorithm for approximating zero points of monotone (not strongly monotone) and bounded mapping is established and analyzed. The algorithm is proved to converge strongly to x * ∈ A − 1 ( 0 ) which is not involving the resolvent operator. Moreover, applications to solutions of variational inequality problems, convex minimization problems and a cluster of semi-pseudo mappings are included. Numerical results are reported to illustrate the behavior of the algorithm with different sequences of stepsizes and also to compare it with other algorithms.