Strong convergence of resolvents of monotone operators in banach spaces

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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 ≠ 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.

Original languageEnglish
Pages (from-to)755-758
Number of pages4
JournalProceedings of the American Mathematical Society
Volume103
Issue number3
DOIs
Publication statusPublished - 1988
Externally publishedYes

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Keywords

  • Iteration
  • Monotone operator
  • Nearest point
  • Resolvent

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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