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Introduction Into The Theory Of Monotone And Accretive Operators

In: Nonlinear Ill-posed Problems of Monotone Type

Author

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  • YAKOV ALBER
  • IRINA RYAZANTSEVA

Abstract

Let X be a real linear normed space, ∥x∥ be a norm of an element x in X, θx be an origin of X. Strong convergence xn → x, n = 0, 1, ., of the sequence {xn} ⊂ X to x ∈ X means that ∥xn −x∥ → 0 as n→∞. In this case, x is a (strong) limit point of the sequence {xn}. If {xn} converges strongly to x ∈ X then 1) any subsequence {xnk} ⊂ {xn} also converges to the same point, 2) the sequence {∥xn − ξ∥} is bounded for any ξ ∈ X.

Suggested Citation

  • Yakov Alber & Irina Ryazantseva, 2006. "Introduction Into The Theory Of Monotone And Accretive Operators," Springer Books, in: Nonlinear Ill-posed Problems of Monotone Type, pages 1-116, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4020-4396-3_1
    DOI: 10.1007/1-4020-4396-1_1
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