Total Asymptotically Nonexpansive Mappings and Generalized Variational Inclusion Problems: Algorithmic and Analytical Approach

• Published in: Numerical functional analysis and optimization Vol. 44; no. 9; pp. 906 - 953
• Main Authors: Balooee, Javad, Chang, Shih-sen, Liu, Min, Yao, Jen-Chih
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 04.07.2023; Taylor & Francis Ltd
• Subjects: Asymptotic properties; Banach spaces; generalized variational inclusion problem; H(.,.)-accretive operator; Iterative algorithms; Mathematical analysis; P-η-accretive mapping; resolvent method; resolvent operator; total asymptotically nonexpansive mapping
• ISSN: 0163-0563; 1532-2467
• DOI: 10.1080/01630563.2023.2209147

In this article, we pursue two goals. First, a new iterative scheme based on the resolvent operator method for finding a common element of the set of solutions of a generalized variational inclusion problem and the set of fixed points of a total asymptotically nonexpansive mapping in a real Banach space is constructed. Under some parameters controlling conditions, the strong convergence of the sequence generated by our proposed iterative algorithm to a common element of the above-mentioned two sets is proved. Our second purpose is to investigate and analyze the concept of H(.,.)-accretive operator that appeared in the literature and to point out some comments concerning it. Several new examples are also provided.