Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 75, Issue 12, Pages 4699-4710Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2011.12.007
Keywords
Asymptotic linearity; Hadamard differentiable; Nemytskii operator
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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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