Theory of functions, functional analysis, statistics, probability

Previous and Current Research

Main directions:

Complex polynomial approximation,

Extension from an arbitrary set E ⊂ R of functions, belonging to Sobolev, Helder, generalized Helder classes ,

Shape Preserving Approximation.

Boundary and extremal problems.

Other results:

Sewell’s, Hasson’s, DeVore and Yu’s, Dzyadyk and Korneichuk’s and other problems are solved.

Soros grants, France – Ukrainian grant “Dnipro”, dozens “travel grants” from

leading universities of North America, Europe, Asia and Israel.

Future Projects and Goals

The project, supported by the NRFU: Support for research by leading and young scientists. The title (goal): Best constrained and unconstrained approximation by polynomials and ... .

Selected Publications

50 publications in

https://publons.com/researcher/1932543/igor-shevchuk/publications/

53 documents in

https://www.scopus.com/authid/detail.uri?authorId=16522008000

Other selected publications

Uniform and pointwise shape preserving approximation (SPA) by algebraic polynomials: an update. The SMAI journal of computational mathematics, 5 (2019) , 99-108 (with K. A. Kopotun and D.Leviatan).

Jackson type estimates for piecewise q-monotone approximation, q ≥ 3, are not valid, PAFA, 1, (2016), N1, 85-96 (with D.Leviatan).

Uniform and pointwise shape preserving approximation by algebraic polynomials. Surveys in Appr. Th. 6 (2011), 24-74. (with K. A. Kopotun, D. Leviatan and A. Prymak).

One construction of cubic convex spline, Approximation and optimization, Vol. I, 357-368, Transilvania, Cluj-Napoca, 1997.

Comonotone approximation, Fundamentalnaya i prikladnaya matematika, 2(1996), 319-363 (in Russian, with Gilewicz J.)

Approximation by polynomials and traces of functions, continuous on the segment, Kyiv, Naukova dumka, 1992, 225 p. (in Russian)

On the sharpness of an approximation criterion of smoothness for functions on a segment, Approximation and function spaces, Banach Cent. Publ. 22 (1989), 401-411.

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