Andrii Shidlich
@imath.kiev.ua
Departments of Theory of Functions
Institute of Mathematics of the National Academy of Sciences of Ukraine
RESEARCH, TEACHING, or OTHER INTERESTS
Analysis
Scopus Publications
Scholar Citations
Scholar h-index
Scholar i10-index
Scopus Publications
Viktor V. Savchuk, Stanislav O. Chaichenko, and Andrii L. Shydlich
Springer Science and Business Media LLC
Jürgen Prestin, Viktor Savchuk, and Andrii Shidlich
Elsevier BV
S. O. Chaichenko, A. L. Shidlich, and T. V. Shulyk
Springer Science and Business Media LLC
A.S. Serdyuk and A.L. Shidlich
Vasyl Stefanyk Precarpathian National University
Direct and inverse approximation theorems are proved in the Besicovitch-Stepanets spaces $B{\\mathcal S}^{p}$ of almost periodic functions in terms of the best approximations of functions and their generalized moduli of smoothness.
F. G. Abdullayev, A. S. Serdyuk, and A. L. Shidlich
Springer Science and Business Media LLC
Fahreddin Abdullayev, Stanislav Chaichenko, Meerim Imashkyzy, and Andrii Shidlich
Rocky Mountain Mathematics Consortium
In the Musielak-Orlicz type spaces ${\\mathcal S}_{\\bf M}$, exact Jackson-type inequalities are obtained in terms of best approximations of functions and the averaged values of their generalized moduli of smoothness. The values of Kolmogorov, Bernstein, linear, and projective widths in ${\\mathcal S}_{\\bf M}$ are found for classes of periodic functions defined by certain conditions on the averaged values of the generalized moduli of smoothness.
Fahreddin Abdullayev, Stanislav O. Chaichenko, and Andriy L. Shidlich
Element d.o.o.
In Musilak-Orlicz type spaces ${\\mathcal S}_{\\bf M}$, direct and inverse approximation theorems are obtained in terms of the best approximations of functions and generalized moduli of smoothness. The question of the exact constants in Jackson-type inequalities is studied.
Stanislav Chaichenko, Viktor Savchuk, and Andrii Shidlich
Springer Science and Business Media LLC
Fahreddin ABDULLAYEV, Stanislav CHAICHENKO, Meerim IMASH KYZY, and Andrii SHIDLICH
The Scientific and Technological Research Council of Turkey (TUBITAK-ULAKBIM) - DIGITAL COMMONS JOURNALS
In weighted Orlicz-type spaces Sp,μ with a variable summation exponent, the direct and inverse approximation theorems are proved in terms of best approximations of functions and moduli of smoothness of fractional order. It is shown that the constant obtained in the inverse approximation theorem is the best in a certain sense. Some applications of the results are also proposed. In particular, the constructive characteristics of functional classes defined by such moduli of smoothness are given. Equivalence between moduli of smoothness and certain Peetre K-functionals is shown in the spaces Sp,μ.
Stanislav Chaichenko, Andrii Shidlich, and Fahreddin Abdullayev
Walter de Gruyter GmbH
AbstractIn the Orlicz type spaces 𝓢M, we prove direct and inverse approximation theorems in terms of the best approximations of functions and moduli of smoothness of fractional order. We also show the equivalence between moduli of smoothness and PeetreK-functionals in the spaces 𝓢M.
Stanislav O. Chaichenko and Andrii L. Shydlich
Springer Science and Business Media LLC
Fahreddin Abdullayev, Pelin Özkartepe, Viktor Savchuk, and Andrii Shidlich
National Library of Serbia
In the paper, exact constants in direct and inverse approximation theorems for functions of several variables are found in the spaces Sp. The equivalence between moduli of smoothness and some K-functionals is also shown in the spaces Sp.
, Jurgen Prestin, , Viktor Savchuk, , Andrii Shidlich, and
Babes-Bolyai University Cluj-Napoca
We obtain direct and inverse approximation theorems of functions of several variables by Taylor-Abel-Poisson means in the integral metrics. We also show that norms of multipliers in the spaces $L_{p,Y}(\\mathbb T^d)$ are equivalent for all positive integers $d.$
J. Prestin, V. V. Savchuk, and A. L. Shidlich
Springer Science and Business Media LLC
A. L. Shidlich and S. O. Chaichenko
Informa UK Limited
We obtain the exact values of some important approximative quantities (such as the best approximation, the basis width, Kolmogorov's width, and the best n-term approximation) of certain sets of images of the diagonal operators in the Orlicz sequence spaces l M .
Andriy L. Shidlich and Stanislav O. Chaichenko
Element d.o.o.
We obtain some new inequalities of Chebyshev Type. Mathematics subject classification (2010): 26D15.
Viktor V. Savchuk and Andriy L. Shidlich
Springer Science and Business Media LLC
In the spaces S ^p of functions of several variables, 2 π -periodic in each variable, we study the approximative properties of operators A _ϱ, r ^Δ and P _ϱ, s ^Δ , which generate two summation methods of multiple Fourier series on triangular regions. In particular, in the terms of approximation estimates of these operators, we give a constructive description of classes of functions, whose generalized derivatives belong to the classes S ^p H _ω.
Andriy L. Shidlich
Element d.o.o.
We obtain necessary and sufficient conditions for validity of some Chebyshev-Type inequalities.
A.I. Stepanets and A.L. Shidlich
Elsevier BV
Alexander I Stepanets and Andrey L Shidlich
Steklov Mathematical Institute
We study the numbers that characterize the best approximation of the integrals of functions in , , by integrals of rank . We find exact values and orders as for the least upper bounds of these numbers on the classes of functions representable as products of a fixed non-negative function and functions in the unit ball of . The numbers are used to obtain necessary and sufficient conditions for an arbitrary function in to lie in , . We discuss applications of the results obtained to the approximation of measurable functions (given by convolutions with summable kernels) by entire functions of exponential type.
A. L. Shydlich
Springer Science and Business Media LLC
A. I. Stepanets, A. S. Serdyuk, and A. L. Shidlich
Springer Science and Business Media LLC
A. I. Stepanets, A. S. Serdyuk, and A. L. Shidlich
Springer Science and Business Media LLC
A. L. Shydlich
Springer Science and Business Media LLC
A. I. Stepanets and A. L. Shidlich
Springer Science and Business Media LLC