Differentiability Properties of Lipschitzian Bilinear Operators in Real Normed Spaces

Kazuhisa Nakasho; Yasunari Shidama

doi:10.2478/forma-2024-0013

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Differentiability Properties of Lipschitzian Bilinear Operators in Real Normed Spaces

Formalized Mathematics

Volume 32 (2024): Issue 1 (August 2024)

By: Kazuhisa Nakasho and Yasunari Shidama

Open Access

|Dec 2024

Abstract

This article is devoted to the Mizar formalization of various properties of differentiability of Lipschitzian bilinear operators in real normed spaces. Main results include the Lipschitz continuity of partial derivatives, the representation of the total derivative in terms of partial derivatives, and the continuous differentiability of Lipschitzian bilinear operators on open subsets of the product space.

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Articles in this issue

DOI: https://doi.org/10.2478/forma-2024-0013 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630

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Language: English

Page range: 165 - 172

Accepted on: Dec 9, 2024

Published on: Dec 31, 2024

Published by: University of Białystok

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

bilinear operator,

Lipschitz continuity,

normed space

Related subjects:

Mathematics,

Logic and set theory,

Computer sciences,

Artificial intelligence

© 2024 Kazuhisa Nakasho, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

Volume 32 (2024): Issue 1 (August 2024)