Dzyubenko German A.

In 1981 he entered the 3rd (radio-technical) faculty of the Kiev Higher Military Anti-Aircraft Missile Engineering S. M. Kirov School and in 1989 graduated from the Faculty of Physics and Mathematics of the National Pedagogical Dragomanov University.

In 1985 he served in the army.

Since 2018 he has been working at the Institute of Mathematics of the National Academy of Sciences of Ukraine.

In 2010 he was awarded the title of Senior scientific researcher in the specialty "Mathematical Analysis".

1. Shape preserving approximation of piecewise monotone and piecewise positive functions, thesis of Candidate of Physical and Mathematical Sciences (equiv. Ph.D. in Math), Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, 1994.

2. Shape preserving approximation of functions, thesis of Doctor of Physical and Mathematical Sciences, Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, 2019.

Shape preserving approximation (SPA)

The following results are proved.

-- for approximation by algebraic polynomials the classical (in form) pointwise estimates of piecewise convex SPA, the interpolation (at the ends of an interval) pointwise estimate of piecewise monotone SPA and the pointwise estimates of piecewise positive, piecewise monotone and piecewise convex nearly SPA (i.e. when the polynomial is allowed not to preserve the shape of the function in small neighborhoods of the points of its change).
-- for approximation by trigonometric polynomials the classical uniform estimates of SPA; it is strengthened the known estimates and initiated nearly SPA.
-- it is found splines that provide the best local and global estimates of 3-monotone approximation with different modulus of smoothness and in different metrics.
-- it is constructed counterexamples in cases where the corresponding classical estimates are false and in cases where improving the nature of the dependence of constants on the basic parameters in the obtained estimates is impossible.

--- Third international conference “Curves and Surfaces”, 27 June- 3 July 1996, Chamonix Mont Blanc, France;
--- міжнародній науковій конференції “Теорія наближення функцій та її застосуваня, присв’ячена пам'яті В.К.Дзядика”, 27-31 Травень 1999, Київ, Ін-т математики НАН України;
--- міжнародній науковій конференції “Functional Methods in Approx. Theory, Operator Theory, Stochastic
Analysis and Statistics” (FM2001), 19-22 October 2001, Kyiv, Ukraine;
--- міжнародній науковій конференції пам'яті В.Я.Буняковского (1804-1889) “Bunyakovsky Intern. Conf.”, August 16-21, 2004, Kyiv, Ukraine;
--- міжнародній науковій конференції “Functional Methods in Approximation Theory, Operator Theory, Stochastic Analysis and statistics II, dedicated to the memory of A.Ya. Dorogovtsev (1935-2004)” (FM2004), October 1-5, 2004, Kyiv, Ukraine;
--- MITACS 2007 Joint Conference of Canadian Mathematical Society, May 31-June 3, Winnipeg, Manitoba, Canada;
--- 9th Conference on “Orthogonal Polynomials, Special Functions and Applications”, July, 2nd-6th 2007 – Marseille, France;
--- міжнародній науковій конференції “Functional Methods in Approximation Theory and Operator Theory III, dedicated to the memory of V. K. Dzyadyk (1919-1998)” (FM2009), August 22-26, 2009, Camp Hart, Village Svityaz, Shatskyi Region, Volyn, Ukraine;
--- Canadian Mathematical Society Summer Meeting, The Delta Winnipeg, Manitoba, Canada – 2014 June 6-9, cms.math.ca;
--- Final AMMODIT Conference "Mathematics for Life Sciences", March 18-22, 2019, Kyiv, Ukraine;
--- Конф. "Теорія наближень і її застосування", 3–5 жовтня 2019 р., м. Дніпро;
--- Конф. “Сучасні проблеми диф. рівнянь та їх заст-я”, присв. 100-річчю від ня нар. С.Д. Ейдельмана, м. Чернівці, 16-19 вересня 2020 р.;
--- Міжнар. конф. до 100 річчя із дня народження М. П. Корнєйчука (1920–2003), «ТЕОРІЯ НАБЛИЖЕНЬ І ЇЇ ЗАСТОСУВАННЯ», м. Дніпро,16-19 вересня 2020 р.;
--- 11th Intern. Skorobohatko Math. Conf., Lviv, October 26–30, 2020;