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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Approximating zeros of accretive operators


Author: Simeon Reich
Journal: Proc. Amer. Math. Soc. 51 (1975), 381-384
MSC: Primary 47H05
DOI: https://doi.org/10.1090/S0002-9939-1975-0470762-1
MathSciNet review: 0470762
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Abstract: Let $ A$ be an $ m$-accretive set in a reflexive Banach space $ E$ with a Gateaux differentiable norm. For positive $ r$ let $ {J_r}$ denote the resolvent of $ A$. If the duality mapping of $ E$ is weakly sequentially continuous and 0 is in the range of $ A$, then for each $ x$ in $ E$ the strong $ {\lim _{r \to \infty }}{J_r}x$ exists and belongs to $ {A^{ - 1}}(0)$. This is an extension to a Banach space setting of a result previously known only for Hilbert space.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0470762-1
Keywords: Accretive, duality mapping, nonexpansive retract, strong and weak convergence
Article copyright: © Copyright 1975 American Mathematical Society