INTRODUCTION INTO THE THEORY OF MONOTONE AND ACCRETIVE OPERATORS

Yakov Alber and Irina Ryazantseva

A chapter in Nonlinear Ill-posed Problems of Monotone Type, 2006, pp 1-116 from Springer

Abstract: 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.

Keywords: Banach Space; Variational Inequality; Duality Mapping; Monotone Operator; Maximal Monotone (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4020-4396-3_1

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DOI: 10.1007/1-4020-4396-1_1

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