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Iterative solutions for zeros of accretive operators
Author(s) -
Dominguez Benavides Tomas,
Lopez Acedo Genaro,
Xu Hong–Kun
Publication year - 2003
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310003
Subject(s) - mathematics , resolvent , convergence (economics) , resolvent formalism , banach space , rate of convergence , scheme (mathematics) , iterative and incremental development , iterative method , pure mathematics , mathematical analysis , mathematical optimization , finite rank operator , computer science , computer network , software engineering , channel (broadcasting) , economics , economic growth
Two iterative schemes are designed to approach zeros of m –accretive operators in Banach spaces. The first one is a kind of contractive iteration process involving with the resolvent and the second one is an averaged iteration process of the identity and the resolvent. Strong convergence for the first scheme and weak convergence for the second scheme are proved. The second scheme is also shown to have superlinear rate of convergence.