Dnipro University Mathematics Bulletin
https://vestnmath.dnu.dp.ua/index.php/dumb
<table><tbody><tr><td><img src="/files/pics/gen_issue_cover.png" alt="" width="100px" height="150px" /></td><td style="padding-left: 16px; vertical-align: top;"><p>The journal presents results of researches concerning algebra, approximation theory for the functions of real variable, the equations of mathematical physics, and their application to problem solution.</p><p>The journal is intended for research officers, post-graduate and undergraduate students.</p></td></tr></tbody></table>Oles Honchar Dnipro National Universityen-USDnipro University Mathematics Bulletin2312-9557Authors who publish with this journal agree to the following terms:<ol><li>Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a <a href="http://creativecommons.org/licenses/by/3.0/" target="_new">Creative Commons Attribution License</a> that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.</li><li>Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.</li><li>Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See <a href="http://opcit.eprints.org/oacitation-biblio.html" target="_new">The Effect of Open Access</a>).</li></ol>On the best polynomial approximation of $$$(\psi,\beta)$$$-differentiable functions in $$$L_2$$$ space
https://vestnmath.dnu.dp.ua/index.php/dumb/article/view/81
On the classes $$$L^{\psi}_{\beta,2}$$$ exact estimates have been obtained for the values of the best polynomial approximations of $$$(\psi,\beta)$$$-differentiable functions, expressed by the averages modulus of continuity $$$\widehat{\omega}(f^{\psi}_{\beta},t)$$$ with a weight $$$\xi(t)$$$. This modulus was introduced by K.V. Runovski and H.J. Schmeisser.S.B. Vakarchuk
Copyright (c) 2017 S.B. Vakarchuk
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2017-06-262017-06-2625313On average $$$n$$$-widths of certain classes of functions in $$$L_2(\mathbb{R})$$$ space
https://vestnmath.dnu.dp.ua/index.php/dumb/article/view/82
На классах функций $$$\mathcal{W}^r (\omega_m;\Phi)$$$, где $$$r, m\in \mathbb{N}$$$, $$$\Phi$$$ — мажоранта, $$$\omega_m$$$ — модуль непрерывности m-го порядка, получены оценки сверху и снизу колмогоровского, линейного и бернштейновского средних $$$\nu$$$-поперечников. Также приведено условие, при выполнении которого из указанного результата следуют точные значения перечисленных экстремальных характеристик.S.B. VakarchukM.B. Vakarchuk
Copyright (c) 2017 S.B. Vakarchuk, M.B. Vakarchuk
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2017-06-262017-06-26251422Sharp Remez-type inequalities of various metrics for the best approximations by a constant
https://vestnmath.dnu.dp.ua/index.php/dumb/article/view/83
We prove new sharp Remez-type inequalities of various metrics on the sets of functions with a given comparison function.A.Ye. HaidaburaV.A. Kofanov
Copyright (c) 2017 A.Ye. Haidabura, V.A. Kofanov
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2017-06-262017-06-26252332On the optimal renewal of n-linear functionals from linear information on the sets, defined by unbounded operators
https://vestnmath.dnu.dp.ua/index.php/dumb/article/view/84
We found the optimal linear information and the optimal method of its use to renew the n-linear functionals on sets which are defined by unbounded operators.M.S. Gun'koA.A. Rudenko
Copyright (c) 2017 M.S. Gun'ko, A.A. Rudenko
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2017-06-262017-06-26253340Solution of Bojanov-Naidenov problem with constraints for the norm $$$\|x\|_{p,\delta} = \sup \bigl\{ \| x \|_{L_p[a;b]} \colon a,b\in \mathbb{R}, b-a\leqslant \delta \bigr\}$$$
https://vestnmath.dnu.dp.ua/index.php/dumb/article/view/85
For given $$$r\in \mathbb{N}$$$; $$$p,\lambda > 0$$$ and fixed interval $$$[a;b] \subset \mathbb{R}$$$ we solve the extremal problems 1) $$$\int\limits_a^b |x(t)|^q dt \rightarrow \sup$$$, $$$q > p$$$, 2) $$$\int\limits_a^b |x^{(k)}(t)|^q dt \rightarrow \sup$$$, $$$q \geqslant 1$$$, $$$k\in \mathbb{N}$$$, $$$k < r$$$, on the set of functions $$$f\in L^r_{\infty}$$$ such that $$$\|x^{(r)}\|_{\infty} \leqslant 1$$$, $$$\|x\|_{p,\delta} \leqslant \| \varphi_{\lambda,r} \|_{p,\delta}$$$, $$$\delta \in (0,\pi / \lambda)$$$.V.A. Kofanov
Copyright (c) 2017 V.A. Kofanov
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2017-06-262017-06-26254150Integral representation of positive definite kernels, associated with differential expression of second order of elliptic type
https://vestnmath.dnu.dp.ua/index.php/dumb/article/view/86
We obtain the integral representation of positive definite kernels of the two variables associated with differential expression of second order of elliptic type.O.V. Lopotko
Copyright (c) 2017 O.V. Lopotko
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2017-06-262017-06-26255156Properties and approximation of integrable functions
https://vestnmath.dnu.dp.ua/index.php/dumb/article/view/87
Some properties of the functions integrable on the segment were considered in this article. Estimates for approximation are obtained.V.P. MotornyiU.P. BabyakK.R. StudenikinaM.V. Shtats'ka
Copyright (c) 2017 V.P. Motornyi, U.P. Babyak, K.R. Studenikina, M.V. Shtats'ka
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2017-06-262017-06-26255767On extremal subspaces for widths of classes of convolutions
https://vestnmath.dnu.dp.ua/index.php/dumb/article/view/88
We obtained the exact values of the best $$$L_1$$$-approximations of the classes $$$K*F$$$ ($$$r\in \mathbb{N}$$$) of periodic functions $$$K*f$$$ such that $$$f$$$ belongs to a given rearrangement-invariant set $$$F$$$ and $$$K$$$ is $$$2\pi$$$-periodic, not increasing oscillation, kernel, by subspaces of generalized polynomial splines with nodes at points $$$2k\pi / n$$$ ($$$n\in \mathbb{N}$$$, $$$k\in \mathbb{Z}$$$). It is shown that these subspaces are extremal for the Kolmogorov widths of the corresponding functional classes.N.V. Parfinovich
Copyright (c) 2017 N.V. Parfinovich
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2017-06-262017-06-26256879Improvement of smoothness of functions by bilinear operators, continuous by measure
https://vestnmath.dnu.dp.ua/index.php/dumb/article/view/89
The sequences of the translation invariant by the both arguments, continuous bilinear operators $$$T_n\colon L_1 \times L_1 \rightarrow L_0$$$ has been considered. The improvement of the smoothness of the functions belonging to the Lipschitz-Holder classes has been established.A.M. Pas'ko
Copyright (c) 2017 A.M. Pas'ko
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2017-06-262017-06-26258083Traces of generalized potentials
https://vestnmath.dnu.dp.ua/index.php/dumb/article/view/90
The theorem on finding traces of integral operators defined on a symmetric space with a certain kernel is obtained using the Krein-Semenov interpolation theorem.B.I. PeleshenkoT.N. Semirenko
Copyright (c) 2017 B.I. Peleshenko, T.N. Semirenko
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2017-06-262017-06-26258488On locally finite groups whose cyclic subgroups are monopronormal
https://vestnmath.dnu.dp.ua/index.php/dumb/article/view/91
The description of locally finite groups whose cyclic subgroups are monopronormal was obtained.A.A. Pypka
Copyright (c) 2017 A.A. Pypka
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2017-06-262017-06-26258996Criterions for the best non-symmetric $$$L_p$$$- and $$$L_1$$$-approximant for the functions with values in KB-spaces with weight
https://vestnmath.dnu.dp.ua/index.php/dumb/article/view/92
The questions of the characterization of the best non-symmetric $$$L_p$$$ and $$$L_1$$$-approximant for the functions with values in KB-space with a weight were considered. The criterions of the best non-symmetric approximant for the specified functions in metrics of the spaces $$$L_p$$$ and $$$L_1$$$ with a weight is obtained.M.Ye. TkachenkoV.M. Traktyns'ka
Copyright (c) 2017 M.Ye. Tkachenko, V.M. Traktyns'ka
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2017-06-262017-06-262597102