Strong convergence of resolvents of monotone operators in banach spaces

Kazuo Kido

doi:10.1090/S0002-9939-1988-0947652-x

Strong convergence of resolvents of monotone operators in banach spaces

Kazuo Kido

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

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 ≠ φ. Fix x ∊ E. Then J_λx converges strongly to Px as λ→∞, where J_λ is the resolvent of A, and P is the nearest point mapping from E onto A^-10.

Original language	English
Pages (from-to)	755-758
Number of pages	4
Journal	Proceedings of the American Mathematical Society
Volume	103
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-1988-0947652-x
Publication status	Published - 1988 Jul
Externally published	Yes

Keywords

Iteration
Monotone operator
Nearest point
Resolvent

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-1988-0947652-x

Cite this

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abstract = "Let E* be a real strictly convex dual Banach space with a Fr{\'e}chet differentiable norm, and A a maximal monotone operator from E into E* such that A-1 ≠ φ. Fix x ∊ E. Then Jλx converges strongly to Px as λ→∞, where Jλ is the resolvent of A, and P is the nearest point mapping from E onto A-10.",

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N2 - 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 ≠ φ. Fix x ∊ E. Then Jλx converges strongly to Px as λ→∞, where Jλ is the resolvent of A, and P is the nearest point mapping from E onto A-10.

AB - 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 ≠ φ. Fix x ∊ E. Then Jλx converges strongly to Px as λ→∞, where Jλ is the resolvent of A, and P is the nearest point mapping from E onto A-10.

KW - Iteration

KW - Monotone operator

KW - Nearest point

KW - Resolvent

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JF - Proceedings of the American Mathematical Society

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ER -

Strong convergence of resolvents of monotone operators in banach spaces

Abstract

Keywords

ASJC Scopus subject areas

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