Convergence analysis of new inertial method for the split common null point problem. (9th December 2022)

• Record Type: Journal Article
• Authors: Ogbuisi, Ferdinard U.; Shehu, Yekini; Yao, Jen-Chih
• Is Part Of: Optimization. Volume 71:Number 13(2022)
• Page Start: 3767
• Page End: 3795
• Publication Date: 2022-12-09
• Subjects: Alternated inertial method -- inverse strongly monotone operator -- split common null point problem -- bounded linear operator -- Hilbert spaces; 49J53 -- 65K10 -- 49M37 -- 90C25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1914035
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we propose a new iterative method with alternated inertial step for solving split common null point problem in real Hilbert spaces. We obtain weak convergence of the proposed iterative algorithm. Furthermore, we introduce the notion of bounded linear regularity property for the split common null point problem and obtain the linear convergence property for the new algorithm under some mild assumptions. Finally, we provide some numerical examples to demonstrate the performance and efficiency of the proposed method.