On sufficient conditions ensuring the norm convergence of an iterative sequence to zeros of accretive operators

Huanhuan Cui and Menglong Su

Applied Mathematics and Computation, 2015, vol. 258, issue C, 67-71

Abstract: Given two real sequences (rn) and (αn), we study the iterative scheme: xn+1=αnu+(1-αn)Jrnxn, for finding a zero of an accretive operator A, where u is a fixed element and Jrn denotes the resolvent of A. To ensure its convergence, the real sequence (rn) is always assumed to satisfy ∑n=0∞|rn+1-rn|<∞. In this paper we show this condition can be completely removed, which enables us to improve a result recently obtained by Saejung.

Keywords: Accretive operator; Resolvent; Yosida approximation; Uniform convexity (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:258:y:2015:i:c:p:67-71

DOI: 10.1016/j.amc.2015.01.108

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