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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2011, Issue 1, Pages 87–98
(Mi vuu209)
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This article is cited in 2 scientific papers (total in 2 papers)
MATHEMATICS
On the space of regular smooth functions
V. I. Rodionov Udmurt State University, Faculty of Information Technologies and Computer Engineering, Izhevsk, Russia
Abstract:
The concept of regular smooth function is defined. Any piecewise smooth function is regular smooth function, and any regular smooth function is Lipschitzian. Any regular smooth function has finite one-sided derivatives: the left-side derivative is continuous at the left and the right-side derivative is continuous on the right. One-sided derivatives generate concept of a regular derivative. The space of regular smooth functions is the closureof the space of piecewise linear functions on norm of space Lipschitzian functions. The space of piecewise smooth functions is everywhere dense in space of regular smooth functions. The analogue of the equation of Euler for the elementary variational problem in space of regular smooth functions is proved.
Keywords:
one-sided derivative, piecewise smooth function, Lipschitzian function, regulated function, calculus of variations.
Received: 29.01.2010
Citation:
V. I. Rodionov, “On the space of regular smooth functions”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 1, 87–98
Linking options:
https://www.mathnet.ru/eng/vuu209 https://www.mathnet.ru/eng/vuu/y2011/i1/p87
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Abstract page: | 434 | Full-text PDF : | 238 | References: | 48 | First page: | 1 |
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