Quantitative asymptotic regularity of the VAM iteration with error terms for $m$-accretive operators in Banach spaces

Paulo Firmino; Laurenţiu Leuştean

doi:10.4171/zaa/1772

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Quantitative asymptotic regularity of the VAM iteration with error terms for $m$ -accretive operators in Banach spaces

Paulo Firmino
Universidade de Lisboa, Lisboa, Portugal
Laurenţiu Leuştean
University of Bucharest, Bucharest, Romania; Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania; Institute for Logic and Data Science, Bucharest, Romania

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Abstract

In this paper, we obtain, by using proof mining methods, quantitative results on the asymptotic regularity of the viscosity approximation method (VAM) with error terms for $m$ -accretive operators in Banach spaces. For concrete instances of the parameter sequences, linear rates are computed by applying a lemma due to Sabach and Shtern.

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Paulo Firmino, Laurenţiu Leuştean, Quantitative asymptotic regularity of the VAM iteration with error terms for $m$ -accretive operators in Banach spaces. Z. Anal. Anwend. (2024), published online first

DOI 10.4171/ZAA/1772