CONSTRUCTION AND RESEARCH INTO THE OPERATORS OF INTERLINEATION OF THE FUNCTIONS OF TWO VARIABLES ON A SYSTEM OF DISJOINT CURVES WITH THE PRESERVATION OF THE CLASS OF DIFFERENTIABILITY

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DOI https://doi.org/10.15407/pmach2016.03.060
Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 19, no. 3, 2016 (September)
Pages 60-68
Cited by J. of Mech. Eng., 2016, vol. 19, no. 3, pp. 60-68

 

Authors

I. V. Serhiienko, V. M. Glushkov Institute of Cybernetics of the NASU (40, Academician Glushkov Ave., Kyiv, 03187, Ukraine)

O. M. Lytvyn, Ukrainian Engineering Pedagogics Academy (16, Universitetskaya St., Kharkiv, 61003, Ukraine),
e-mail: academ_mail@ukr.net

O. O. Lytvyn, Ukrainian Engineering Pedagogics Academy (16, Universitetskaya St., Kharkiv, 61003, Ukraine),
e-mail: academ_mail@ukr.net

O. V. Tkachenko, Zaporozhye Machine-Building Design Bureau Progress State Enterprise named after
Academician A. G. Ivchenko (2, Ivanova Str., 69068, Zaporozhye, Ukraine), e-mail: avt2007@outlook.com

O. L. Hrytsai, Zaporozhye Machine-Building Design Bureau Progress State Enterprise named after
Academician A. G. Ivchenko (2, Ivanova Str., 69068, Zaporozhye, Ukraine), e-mail: avt2007@outlook.com

 

Abstract

The interlineation operators of the functions of two variables are constructed and investigated with the preservation of the class of differentiability. To this class belongs the function being approximated, provided that the traces of these operators and the traces of their partial derivatives in one of the variables to a fixed order coincide on a given system of lines with the corresponding traces of the function being approximated.

 

Keywords: class of differentiability, traces of a function, traces of derivatives on a line, Hermitian interlination

 

References

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Received 16 August 2016

Published 30 September 2016