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Proceedings of the American Mathematical Society

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



Weakly closed $ m$-accretive operators

Authors: A. Yamamoto and N. Okazawa
Journal: Proc. Amer. Math. Soc. 66 (1977), 284-288
MSC: Primary 47H05; Secondary 47H15
MathSciNet review: 0467409
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Abstract: Let A and B be weakly closed, nonlinear m-accretive (single-valued) operators in a reflexive Banach space X, and $ {B_n}$ be the Yosida approximation of B. Then the following condition is sufficient for the sum $ A + B$ to be also m-accretive: For each $ v \in X,\left\Vert {{B_n}{u_n}} \right\Vert$ is bounded as n tends to infinity, where $ {u_n}$ is defined by the equation $ {u_n} + A{u_n} + {B_n}{u_n} = v,n = 1,2, \ldots $. Some related conditions are also provided.

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Keywords: Nonlinear accretive operator, weak closedness, Yosida approximation, perturbation
Article copyright: © Copyright 1977 American Mathematical Society

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