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
30
Scopus Publications
299
Scholar Citations
11
Scholar h-index
13
Scholar i10-index
Scopus Publications
- Extreme problems of weight approximation on the real axis
Viktor V. Savchuk, Stanislav O. Chaichenko, and Andrii L. Shydlich
Springer Science and Business Media LLC - Approximation on hexagonal domains by Taylor-Abel-Poisson means
Jürgen Prestin, Viktor Savchuk, and Andrii Shidlich
Elsevier BV - Direct and inverse approximation theorems in the weighted orlicz-type spaces with a variable exponent
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. - Direct and Inverse Approximation Theorems in the Besicovitch–Musielak–Orlicz Spaces of Almost Periodic Functions
S. O. Chaichenko, A. L. Shidlich, and T. V. Shulyk
Springer Science and Business Media LLC - Direct and inverse theorems on the approximation of almost periodic functions in Besicovitch-Stepanets spaces
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. - Widths of Functional Classes Defined by the Majorants of Generalized Moduli of Smoothness in the Spaces S<sup>p</sup>
F. G. Abdullayev, A. S. Serdyuk, and A. L. Shidlich
Springer Science and Business Media LLC - Jackson-type inequalities and widths of functional classes in the Musielak–Orlicz type spaces
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. - Direct and inverse approximation theorems of functions in the Musielak-Orlicz type spaces
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. - Approximation of functions by linear summation methods in the Orlicz-type spaces
Stanislav Chaichenko, Viktor Savchuk, and Andrii Shidlich
Springer Science and Business Media LLC - Direct and inverse approximation theorems in the weighted orlicz-type spaces with a variable exponent
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. - Direct and inverse approximation theorems of functions in the Orlicz type spaces S<inf>M</inf>
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. - Approximative Characteristics of Modular Orlicz Spaces
Stanislav O. Chaichenko and Andrii L. Shydlich
Springer Science and Business Media LLC - Exact constants in direct and inverse approximation theorems for functions of several variables in the spaces s<sup>p</sup>
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. - Approximation theorems for multivariate Taylor-Abel-Poisson means
, 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 $d.$ - Direct and Inverse Theorems on the Approximation of 2π-Periodic Functions by Taylor–Abel–Poisson Operators
J. Prestin, V. V. Savchuk, and A. L. Shidlich
Springer Science and Business Media LLC - Approximative Properties of Diagonal Operators in Orlicz Spaces
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 . - On some inequalities of Chebyshev type
Andriy L. Shidlich and Stanislav O. Chaichenko
Element d.o.o.
We obtain some new inequalities of Chebyshev Type. Mathematics subject classification (2010): 26D15. - Approximation of functions of several variables by linear methods in the space S<sup>p</sup>
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. - On necessary and sufficient conditions for validity of some Chebyshev-Type inequalities
Andriy L. Shidlich
Element d.o.o.
We obtain necessary and sufficient conditions for validity of some Chebyshev-Type inequalities. - Best approximations of integrals by integrals of finite rank
A.I. Stepanets and A.L. Shidlich
Elsevier BV - Extremal problems for integrals of non-negative functions
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. - Order equalities for some functionals and their application to the estimation of the best n-term approximations and widths
A. L. Shydlich
Springer Science and Business Media LLC - On relationship between classes of (Ψ, β̄)-differentiable functions and Gevrey classes
A. I. Stepanets, A. S. Serdyuk, and A. L. Shidlich
Springer Science and Business Media LLC - Classification of infinitely differentiable periodic functions
A. I. Stepanets, A. S. Serdyuk, and A. L. Shidlich
Springer Science and Business Media LLC - Saturation of the linear methods of summation of Fourier series in the spaces S <sup>p</sup><inf>φ</inf>
A. L. Shydlich
Springer Science and Business Media LLC
RECENT SCHOLAR PUBLICATIONS
- Approximation of functions by linear methods in weighted Orlicz type spaces with variable exponent
SO Chaichenko, AL Shidlich
Researches in Mathematics 32 (2), 70-87 2024 - Актуальні проблеми теорії наближень в метриках дискретних просторів на множинах сумовних періодичних та майже періодичних функцій
A Serdyuk, A Shidlich
Ukrains’ kyi Matematychnyi Zhurnal 76 (11), 1653-1690 2024 - Владислав Федорович Бабенко (до 75-річчя від дня народження)
VP Motorny, IO Shevchuk, SB Vakarchuk, AO Korenovskyi, VO Kofanov, ...
Ukrains’ kyi Matematychnyi Zhurnal 76 (10), 1565-1568 2024 - Actual problems of the approximation theory in metrics of discrete spaces on sets of summable periodic and almost periodic functions
A Serdyuk, A Shidlich
arXiv preprint arXiv:2407.04329 2024 - Extreme problems of weight approximation on the real axis
VV Savchuk, SO Chaichenko, AL Shydlich
Journal of Mathematical Sciences 279 (1), 104-114 2024 - Approximation on hexagonal domains by Taylor-Abel-Poisson means
J Prestin, V Savchuk, A Shidlich
Journal of Mathematical Analysis and Applications 529 (2), 127536 2024 - Extremal problems of weighted approximation on the real axis
VV Savchuk, SO Chaichenko, AL Shidlich
arXiv preprint arXiv:2310.13531 2023 - OLEKSANDR IVANOVYCH STEPANETS (on his 80th birthday)
IO Lukovs' kyi, VL Makarov, OM Tymokha, VP Motornyi, IO Shevchuk, ...
UKRAINIAN MATHEMATICAL JOURNAL 74 (5), 661-663 2022 - Direct and inverse approximation theorems in the Besicovitch–Musielak–Orlicz spaces of almost periodic functions
SO Chaichenko, TV Shulyk, AL Shidlich
Український математичний журнал 74 (5), 701-716 2022 - Олександр Іванович Степанець (до 80-річчя від дня народження)
ІО Луковський, ВЛ Макаров, ОМ Тимоха, ВП Моторний, ІО Шевчук, ...
Український математичний журнал 74 (5), 579-581 2022 - Jackson-type inequalities and widths of functional classes in the Musielak–Orlicz type spaces
F Abdullayev, S Chaichenko, M Imashkyzy, A Shidlich
Rocky Mountain Journal of Mathematics 51 (4), 1143-1155 2021 - Поперечники функціональних класів, визначених мажорантами узагальнених модулів гладкості в просторах :
F Abdullayev, A Serdyuk, A Shidlich
Ukrains’ kyi Matematychnyi Zhurnal 73 (6), 723-737 2021 - Direct and inverse theorems on the approximation of almost periodic functions in Besicovitch-Stepanets spaces
A Serdyuk, A Shidlich
arXiv preprint arXiv:2105.06796 2021 - Direct and inverse approximation theorems of functions in the Musielak-Orlicz type spaces
F Abdullayev, S Chaichenko, A Shidlich
Mathematical Inequalities & Applications 24 (2), 323–336 2021 - Problems of approximation theory in abstract linear spaces
AS Serdyuk, AL Shidlich
arXiv preprint arXiv:2104.04252 2021 - Direct and inverse theorems of approximation of functions given on hexagonal domains by the Taylor-Abel-Poisson means
AL Shidlich
Riyaziyyat və Mexanikanın Masir Problemləri mummilli Lider Heydər Əliyevin 2021 - Approximation of functions by linear summation methods in the Orlicz-type spaces
S Chaichenko, V Savchuk, A Shidlich
Journal of Mathematical Sciences 249, 705-719 2020 - Widths of functional classes defined by majorants of generalized moduli of smoothness in the spaces
F Abdullayev, A Serdyuk, A Shidlich
arXiv preprint arXiv:2005.05597 2020 - Direct and inverse approximation theorems in the weighted Orlicz-type spaces with a variable exponent
F Abdullayev, S Chaichenko, M Imash kyzy, A Shidlich
Turkish Journal of Mathematics 44 (1), 284-299 2020 - Direct and inverse approximation theorems of functions in the Orlicz type spaces 𝓢M
S Chaichenko, A Shidlich, F Abdullayev
Mathematica Slovaca 69 (6), 1367-1380 2019
MOST CITED SCHOLAR PUBLICATIONS
- Exact Constants in Direct and Inverse Approximation Theorems for Functions of Several Variables in the Spaces Sp
FG Abdullayev, P Ozkartepe, VV Savchuk, AL Shidlich
Filomat 33 (5), 1471-1484 2019
Citations: 22 - Approximation of functions of several variables by linear methods in the space
VV Savchuk, AL Shidlich
Acta Sci. Math. (Szeged) 80, 477–489 2014
Citations: 22 - On relationship between classes of -differentiable functions and Gevrey classes
AI Stepanets, AS Serdyuk, AL Shidlich
Ukrainian Mathematical Journal 61 (1), 171-177 2009
Citations: 19 - Classification of infinitely differentiable periodic functions
AI Stepanets, AS Serdyuk, AL Shidlich
Ukrainian Mathematical Journal 60 (12), 1982-2005 2008
Citations: 19 - Direct and inverse approximation theorems in the weighted Orlicz-type spaces with a variable exponent
F Abdullayev, S Chaichenko, M Imash kyzy, A Shidlich
Turkish Journal of Mathematics 44 (1), 284-299 2020
Citations: 16 - On some new criteria for infinite differentiability of periodic functions
AI Stepanets, AS Serdyuk, AL Shidlich
Dokl. Nats. Akad. Nauk Ukraine, 22-26 2008
Citations: 16 - Direct and inverse approximation theorems of functions in the Orlicz type spaces 𝓢M
S Chaichenko, A Shidlich, F Abdullayev
Mathematica Slovaca 69 (6), 1367-1380 2019
Citations: 13 - Approximative properties of diagonal operators in Orlicz spaces
AL Shidlich, SO Chaichenko
Numerical Functional Analysis and Optimization 36 (10), 1339-1352 2015
Citations: 12 - Extremal problems for integrals of nonnegative functions
AI Stepanets, AL Shidlich
Izv. Ross. Akad. Nauk Ser. Mat. 74 (3), 169--224 2010
Citations: 12 - Best approximations of integrals by integrals of finite rank
AI Stepanets, AL Shidlich
Journal of Approximation Theory 162 (2), 323-348 2010
Citations: 12 - Extremal problems for integrals of nonnegative functions.
AI Stepanets, AL Shidlich
Dokl. Nats. Akad. Nauk Ukraine, 22–26 2008
Citations: integrals of nonnegative functions. - Best n-term approximations by Λ-methods in the spaces
OI Stepanets', AL Shydlich
Ukrainian Mathematical Journal 55 (8), 1338-1362 2003
Citations: 12 - Direct and inverse approximation theorems of functions in the Musielak-Orlicz type spaces
F Abdullayev, S Chaichenko, A Shidlich
Mathematical Inequalities & Applications 24 (2), 323–336 2021
Citations: 11 - Approximation of functions by linear summation methods in the Orlicz-type spaces
S Chaichenko, V Savchuk, A Shidlich
Journal of Mathematical Sciences 249, 705-719 2020
Citations: 10 - Jackson-type inequalities and widths of functional classes in the Musielak–Orlicz type spaces
F Abdullayev, S Chaichenko, M Imashkyzy, A Shidlich
Rocky Mountain Journal of Mathematics 51 (4), 1143-1155 2021
Citations: 9 - Direct and Inverse Theorems on the Approximation of 2π-Periodic Functions by Taylor-Abel-Poisson Operators.
J Prestin, V Savchuk, A Shidlich
Ukrainian Mathematical Journal 69 (5) 2017
Citations: 8 - Approximation theorems for multivariate Taylor-Abel-Poisson means
J Prestin, V Savchuk, A Shidlich
arXiv preprint arXiv:1901.06275 2019
Citations: 7 - Best n-term approximations by Λ-methods in spaces
AL Shidlich
Extremal Problems in the Theory of Functions and Related Questions 46, 283–306 2003
Citations: 7 - Direct and inverse approximation theorems of functions in the Orlicz type spaces
F Abdullaev, A Shidlich, S Chaichenko
Math. Slovaca 69 (6), 1367-1380 2019
Citations: 6 - Direct and inverse approximation theorems of -periodic functions by Taylor--Abel--Poisson means
J Prestin, V Savchuk, A Shidlich
arXiv preprint arXiv:1609.09615 2016
Citations: 6