Asymptotic linearity and Hadamard differentiability

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.


Published in:
Nonlinear Analysis-Theory Methods & Applications, 75, 4699-4710
Year:
2012
Keywords:
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 Record created 2012-06-29, last modified 2018-03-17


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