Lipschitz stability of operators in Banach spaces
作者： V. Yu. Protasov
DOI: 10.1134/S0081543813010203
关键词: Affine transformation 、 Mathematics 、 Operator (computer programming) 、 Metric (mathematics) 、 Banach space 、 Constant (mathematics) 、 Discrete mathematics 、 Cauchy distribution 、 Type (model theory) 、 Lipschitz continuity
摘要: We consider approximations of an arbitrarymap F: X → Y between Banach spaces and by affine operator A: in the Lipschitz metric: difference F — A has to be continuous with a small constant ɛ > 0. In case = ℝ we show that if can affinely ɛ-approximated on any straight line X, then it globally 2ɛ-approximated X. The 2ɛ is sharp. Generalizations this result arbitrary dual are proved, optimality conditions shown examples. As corollary obtain solution problem stated Zs. Pales 2008. relation our results Ulam-Hyers-Rassias stability Cauchy type equations discussed.
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