Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 0470762
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47H05

Retrieve articles in all journals with MSC: 47H05

Additional Information

Keywords: Accretive, duality mapping, nonexpansive retract, strong and weak convergence
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society