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Proceedings of the American Mathematical Society

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

 

 

Strong convergence of resolvents of monotone operators in Banach spaces


Author: Kazuo Kido
Journal: Proc. Amer. Math. Soc. 103 (1988), 755-758
MSC: Primary 47H05; Secondary 47H15
DOI: https://doi.org/10.1090/S0002-9939-1988-0947652-X
MathSciNet review: 947652
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Abstract: Let $ {E^*}$ be a real strictly convex dual Banach space with a Fréchet differentiable norm, and $ A$ a maximal monotone operator from $ E$ into $ {E^*}$ such that $ {A^{ - 1}}0 \ne \emptyset $. Fix $ x \in E$. Then $ {J_\lambda }x$ converges strongly to $ Px$ as $ \lambda \to \infty $, where $ {J_\lambda }$ is the resolvent of $ A$, and $ P$ is the nearest point mapping from $ E$ onto $ {A^{ - 1}}0$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0947652-X
Keywords: Monotone operator, resolvent, nearest point, iteration
Article copyright: © Copyright 1988 American Mathematical Society