On the Iterations of a Sequence of Strongly Quasi-Nonexpansive Mappings with Applications. (17th February 2020)

• Record Type: Journal Article
• Authors: Khatibzadeh, Hadi; Mohebbi, Vahid
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 3(2020)
• Page Start: 231
• Page End: 256
• Publication Date: 2020-02-17
• Subjects: Convex and pseudo-convex minimization -- equilibrium problem -- fixed point iterative methods -- Halpern regularization -- strongly quasi-nonexpansive sequence of mappings -- proximal point method; 90C25 -- 90C30; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1626419
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this article, we study Δ-convergence of iterations for a sequence of strongly quasi-nonexpansive mappings as well as the strong convergence of the Halpern type regularization of them in Hadamard spaces. Then, we give some their applications to iterative methods, convex and pseudo-convex minimization (proximal point algorithm), fixed point theory and equilibrium problems. The results extend several new results in the literature and some of them seem new even in Hilbert spaces. One of our motivations is to unify some usual iterative methods in fixed point theory and proximal methods using the iterations generated by a sequence of strongly nonexpansive mappings.