Abstract
This section is devoted to the fundamental concepts of differentiability and analyticity of mappings from a Banach space X to a Banach space Y. We let L(X, Y) denote the Banach space of bounded linear operators from X to Y with the operator topology. We also assume the reader is familiar with integration of functions with values in a Banach space. For h in a Banach space, the symbol 0(|h|) as |h| → 0 denotes a function such that 0(|h|)/|h| is bounded for h in a neighborhood of zero, o(|h|)denotes a function such that o(|h|)/|h| → 0 as |h| → 0.
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© 1982 Springer-Verlag New York Inc.
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Chow, SN., Hale, J.K. (1982). Elements of Nonlinear Analysis. In: Methods of Bifurcation Theory. Grundlehren der mathematischen Wissenschaften, vol 251. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8159-4_2
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DOI: https://doi.org/10.1007/978-1-4613-8159-4_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-8161-7
Online ISBN: 978-1-4613-8159-4
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