Effective Rates of Convergence for the Resolvents of Accretive Operators. (2nd December 2017)

• Record Type: Journal Article
• Authors: Koutsoukou-Argyraki, Angeliki
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 12(2017)
• Page Start: 1601
• Page End: 1613
• Publication Date: 2017-12-02
• Subjects: Accretive operator -- computable bound extraction -- proof mining -- rate of convergence -- resolvent; 47H04 -- 47H06 -- 03F03 -- 03F10; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1349146
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: We extract explicit, computable, and highly uniform rates for the strong convergence of the resolvents of set-valued, m -accretive, and uniformly accretive at zero/ ϕ -expansive operators on general real Banach spaces to the zero of each operator. This is achieved through proof mining on the proof of a theorem by García–Falset the motivation of which originates from a classical work by Reich. For the bound extraction we make use of a modulus of accretivity at zero, a notion introduced recently by Kohlenbach and the author, as well as a modulus of ϕ -expansivity, a notion introduced analogously here.