Convergence Theorems for Pseudomonotone Equilibrium Problem, Split Feasibility Problem, and Multivalued Strictly Pseudocontractive Mappings. (27th July 2019)

• Record Type: Journal Article
• Authors: Ali, Bashir; Harbau, M. H.
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 10(2019)
• Page Start: 1194
• Page End: 1214
• Publication Date: 2019-07-27
• Subjects: Multivalued strictly pseudocontractive -- pseudomonotone equilibrium problem -- fixed point -- split feasibility problem; 47H09 -- 47J25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1599014
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: Let K be a nonempty closed convex subset of a real Hilbert space H 1 . Let T i : K → CB ( K ), i = 1, 2, …, N be N multivalued strictly pseudocontractive mappings. In this paper, we introduce a new hybrid subgradient method for finding a common point in the set of common fixed points of a finite family of multivalued strictly pseudocontractions, the solution set of class of pseumonotone equilibrium problem and solution set of split feasibility problem. Weak and strong convergence of the iterative sequence are established. Our result is generalization and improvement of several recent results.