Iterative Algorithms for a System of Variational Inclusions Involving Set-Valued Quasi-Contractive Mappings in Banach Spaces. (11th June 2021)

• Record Type: Journal Article
• Authors: Qiu, Yangqing; Liu, Xiaomei
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 8(2021)
• Page Start: 865
• Page End: 882
• Publication Date: 2021-06-11
• Subjects: Convergence -- fixed point -- iterative algorithm -- quasi-contractive mapping -- system of variational inclusions; 47H10 -- 49J30; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1933519
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, a new system of variational inclusions involving set-valued quasi-contractive, lower semi-continuous mappings with nonempty closed and convex values is introduced and studied in real Banach spaces. First, both the existence of fixed points of the set-valued quasi-contractive mappings and the solution of the system of variational inclusions are proved. Then, using the existence result, a new iterative algorithm is constructed. And then the strong convergence of the iterative sequences is proved, and the proof is novel. Finally, a numerical example is given to demonstrate the algorithm. Our results improve and extend some known results.