期刊
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
卷 75, 期 12, 页码 4699-4710出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2011.12.007
关键词
Asymptotic linearity; Hadamard differentiable; Nemytskii operator
For a mapping between Banach spaces, two weaker variants of the usual notion of asymptotic linearity are defined and explored. It is shown that, under inversion through the unit sphere, they correspond to Hadamard and weak Hadamard differentiability at the origin of the inversion. Nemytskii operators from Sobolev spaces to Lebesgue spaces over RN share these weaker properties but they are not asymptotically linear in the usual sense. (C) 2011 Elsevier Ltd. All rights reserved.
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