Ukrains’kyi Matematychnyi Zhurnal
https://umj.imath.kiev.ua/index.php/umj
<h1>Ukrains’kyi Matematychnyi Zhurnal<br>(Ukrainian Mathematical Journal) <br><br></h1> <p>Editor-in-Chief: <a href="https://imath.kiev.ua/~tim/">A. N. Timokha</a><br><br>ISSN: <a href="http://dispatch.opac.d-nb.de/DB=1.1/LNG=EN/CMD?ACT=SRCHA&IKT=8&TRM=0041-6053" target="_blank" rel="nofollow noopener">0041-6053, 1027-3190</a></p> <p>Ukrains'kyi Matematychnyi Zhurnal (UMZh) was founded in May 1949. Journal is issued by <a href="http://imath.kiev.ua/?lang=en" target="_blank" rel="noopener">Institute of Mathematics NAS of Ukraine</a>. English version is reprinted in the Springer publishing house and called <a href="http://link.springer.com/journal/11253" target="_blank" rel="noopener">Ukrainian Mathematical Journal</a>.</p> <p>Ukrains'kyi Matematychnyi Zhurnal focuses on research papers in the principal fields of pure and applied mathematics. The journal is published monthly, each annual volume consists of 12 issues. Articles in Ukrainian and English are accepted for review. </p> <p>UMZh indexed in: <a href="http://www.ams.org/mathscinet/search/journaldoc.html?jc=UKRMJ" target="_blank" rel="nofollow noopener">MathSciNet</a>, <a href="https://zbmath.org/journals/?q=se:00000215" target="_blank" rel="nofollow noopener">zbMATH</a>, <a href="http://www.scopus.com/source/sourceInfo.uri?sourceId=130147&origin=resultslist" target="_blank" rel="nofollow noopener">Scopus</a>, <a href="http://ip-science.thomsonreuters.com/cgi-bin/jrnlst/jlresults.cgi?PC=MASTER&Full=Ukrainian%20Mathematical%20Journal" target="_blank" rel="nofollow noopener">Web of Science</a>, <a href="https://scholar.google.com.ua/citations?hl=uk&user=fZruD2sAAAAJ&view_op=list_works" target="_blank" rel="nofollow noopener">Google Scholar</a>.<br><br><strong>Important information:</strong><br>Regular research articles submitted to UMZh should not exceed 16 pages. The papers accepted for publication usually appear in the printed issue within one year after the decision (there is a queue of accepted articles).<br><br>Ukrains'kyi Matematychnyi Zhurnal encourages authors to submit short communications (up to 6 pages) which are considered as fast track communications and in case of positive decision are published in one of the nearest issues avoiding the general queue of the accepted articles.<br><br>Papers submitted in Ukrainian language and successfuly accepted after peer review appear in one of the nearest issues avoiding the general queue of the accepted articles. <br><br>Ukrains'kyi Matematychnyi Zhurnal considers for publication <em>review articles (up to 35 pages)</em>, i.e. surveys of previously published research on a topic.</p>Institute of Mathematics, NAS of Ukraineen-USUkrains’kyi Matematychnyi Zhurnal1027-3190Fixed-point theorem for an infinite Toeplitz matrix and its extension to general infinite matrices
https://umj.imath.kiev.ua/index.php/umj/article/view/7324
<div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>UDC 517.9</p> </div> </div> </div> <p>In [V. M. Abramov, <em>Bull. Austral. Math. Soc.,</em> <strong>104</strong>, 108–117 (2021)], the fixed-point equation was studied for an infinite nonnegative particular Toeplitz matrix. In the present paper, we provide an alternative proof<span class="Apple-converted-space"> </span>for the existence of a positive solution in the general case.<span class="Apple-converted-space"> </span>The presented proof is based on the application of a version of the<span class="Apple-converted-space"> </span>M. A. Krasnosel'ski fixed-point theorem. The results are then extended to the equations with infinite matrices of a general type.</p>Vyacheslav M. Abramov
Copyright (c) 2024 Vyacheslav Abramov
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2024-03-252024-03-25763315–325315–32510.3842/umzh.v76i3.7324Leonardo and hyper-Leonardo numbers via Riordan arrays
https://umj.imath.kiev.ua/index.php/umj/article/view/7296
<p>UDC 511</p> <p>A generalization of the Leonardo numbers is defined and called the<span class="Apple-converted-space"> </span>hyper-Leonardo numbers.<span class="Apple-converted-space"> </span>Infinite lower triangular matrices, whose elements are Leonardo and hyper-Leonardo numbers are considered.<span class="Apple-converted-space"> </span>Then the $A$- and $Z$-sequences of these matrices are obtained.<span class="Apple-converted-space"> </span>Finally, the combinatorial identities between the hyper-Leonardo and Fibonacci numbers are obtained using the fundamental theorem of the Riordan arrays.</p>Yasemin AlpE. Gokcen Kocer
Copyright (c) 2024 Yasemin ALP, E.Gokcen KOCER
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2024-03-252024-03-25763326–340326–34010.3842/umzh.v45i3.7296A note on the mapping theorem of essential pseudospectra on a Banach space
https://umj.imath.kiev.ua/index.php/umj/article/view/7325
<p>UDC 517.98</p> <p>The main goal<span class="Apple-converted-space"> </span>of the paper is to determine some basic properties of the essential pseudospectrum of a bounded linear operator $A$ defined on a Banach space $X.$<span class="Apple-converted-space"> </span>We also<span class="Apple-converted-space"> </span>prove two different versions of the essential pseudospectral mapping theorem.</p>Aymen AmmarS. Veeramani
Copyright (c) 2024 Veeramani Selvarajan
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2024-03-252024-03-2576334135210.3842/umzh.v76i3.7325Boundary-value problems for the Lyapunov equation. І
https://umj.imath.kiev.ua/index.php/umj/article/view/7785
<p>UDC 517.9</p> <p>We study boundary-value problems for the Lyapunov operator-differential<span class="Apple-converted-space"> </span>equation. By using<span class="Apple-converted-space"> </span>the theory of Moore–Penrose pseudoinverse operators<span class="Apple-converted-space"> </span>and its development, we establish conditions for the existence of generalized solutions and propose algorithms for their construction.</p>O. BoichukYe. PanasenkoO. Pokutnyi
Copyright (c) 2024 Олександр Покутний, Олександр Бойчук, Євгеній Панасенко
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2024-03-252024-03-2576335337210.3842/umzh.v76i3.7785Abelian model structures on comma categories
https://umj.imath.kiev.ua/index.php/umj/article/view/7289
<p>UDC 512.64</p> <p>Let $\mathsf{A}$ and $\mathsf{B}$ be bicomplete Abelian categories, which both have enough projectives and injectives and let $T\colon\mathsf{A}\rightarrow\mathsf{B}$ be a right exact functor. Under some mild conditions, we show that hereditary Abelian model structures on $\mathsf{A}$ and $\mathsf{B}$ can be amalgamated into a global hereditary Abelian model structure on the comma category<span class="Apple-converted-space"> </span>$(T\downarrow\mathsf{B})$. As an application of this result, we give an explicit description of a subcategory that consists of all trivial objects of the Gorenstein flat model structure on the category of modules over a triangular matrix ring.</p>Guoliang Tang
Copyright (c) 2024 guoliang tang
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2024-03-252024-03-2576337338110.3842/umzh.v76i3.7289The norming sets of ${\mathcal L}\big({}^ml_{1}^n\big)$
https://umj.imath.kiev.ua/index.php/umj/article/view/7294
<p>UDC 517.9</p> <p>Let $n\in \mathbb{N},$ $n\geq 2.$ An element $(x_1, \ldots, x_n)\in E^n$ is called a {\em norming point} of $T\in {\mathcal L}(^n E)$ if\/ $\|x_1\| = \ldots = \|x_n\| = 1$ and $|T(x_1, \ldots, x_n)| = \|T\|, $ where ${\mathcal L}(^n E)$ denotes the space of all continuous $n$-linear forms on $E.$ For $T\in {\mathcal L}(^n E),$ we define \begin{align*}{\rm Norm}(T) = \big\{(x_1, \ldots, x_n)\in E^n\colon (x_1, \ldots, x_n) \mbox{is a norming point of} T\big\}.\end{align*} The ${\rm Norm}(T)$ is called the {\em norming set} of $T.$ For $m\in \mathbb{N},$ $m\geq 2, $ we characterize ${\rm Norm}(T)$ for every $T\in {\mathcal L}\big({}^m l_1^n\big),$ where $l_1^n = \mathbb{R}^n$ with the $l_1$-norm. As applications, we classify ${\rm Norm}(T)$ for every $T\in {\mathcal L}\big({}^m l_{1}^n\big)$ with $n = 2, 3$ and $m = 2.$</p>Sung Guen Kim
Copyright (c) 2024 Sung Guen Kim
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2024-03-252024-03-2576338239410.3842/umzh.v76i3.7294Relationship between the Boyanov–Naydenov problem and Kolmogorov-type inequalities
https://umj.imath.kiev.ua/index.php/umj/article/view/7656
<p>UDC 517.5</p> <p>We prove that the Boyanov–Naidenov problem $\|x^{(k)}\|_{q,\, \delta} \to \sup,$ $k= 0,1, \ldots ,r-1,$ on the classes of functions $\Omega^r_p(A_0, A_r) := \{x\in L^r_{\infty}\colon \|x^{(r)}\|_{\infty}\le A_r,\ L(x)_p\le A_0 \},$ where $q \ge 1$ for $k\ge 1$ and $q \ge p$ for $k=0,$ is equivalent to the problem of finding the sharp constant $C = C(\lambda)$ in the Kolmogorov-type inequality \begin{gather}\|x^{(k)}\|_{q,\, \delta} \leq C L(x)_{p}^{\alpha} \big\|x^{(r)}\big\|_\infty^{1-\alpha}, \quad x\in \Omega^{r}_{p, \lambda}, \tag{1}\end{gather} where $\alpha=\dfrac{r-k+1/q}{r+1/p},$ $\|x\|_{p,\, \delta}:=\sup \{\|x\|_{L_p[a,\, b]}\!\colon<span class="Apple-converted-space"> </span>a, b \in {\rm \bf R},\ 0< b-a \le \delta \},$ $\delta > 0,$ $\Omega^{\,r}_{p, \lambda}:= \bigcup \{\Omega^{\,r}_p(A_0, A_r)\colon A_0 = A_r L(\varphi_{\lambda, r})_p \},$ $\lambda > 0,$ $\varphi_{\lambda, r}$ is a contraction of the ideal Euler spline of order $r,$ and $L(x)_p:=\sup\big\{ \|x\|_{L_p[a,\, b]}\colon a, b \in {\rm \bf R},\ |x(t)|>0,\ t\in (a, b)\big\}.$</p> <p>In particular, we obtain a sharp inequality of the form (1) on the classes<span class="Apple-converted-space"> </span>$\Omega^{\,r}_{p, \lambda},$ $\lambda > 0.$ We also prove the theorems on relationships for the Boyanov–Naidenov problems on the spaces of trigonometric polynomials and splines and establish the relevant sharp Bernstein-type inequalities.</p>V. Kofanov
Copyright (c) 2024 Володимир Олександрович Кофанов
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2024-03-252024-03-2576339540410.3842/umzh.v76i3.7656Sufficient conditions and radius problems for the Silverman class
https://umj.imath.kiev.ua/index.php/umj/article/view/7317
<p>UDC 517.5</p> <p>For $0<\alpha\leq1$ and $\lambda>0,$ let \begin{equation}\label{1} G_{\lambda,\alpha}=\left\{f\in\mathcal{A}\colon \left|\frac{1-\alpha+\alpha zf''(z)/f'(z)}{z f'(z)/f(z)}-(1-\alpha)\right|<\lambda,\ z\in\mathbb{D}\right\}.\tag{0.1}\end{equation} The general form of the Silverman class introduced by Tuneski and Irmak [Int. J. Math. and Math. Sci., {\bf 2006}, Article~ID 38089 (2006)].<span class="Apple-converted-space"> </span>Our differential inequality formulation lays out several sufficient conditions for this class.<span class="Apple-converted-space"> </span>Further, we consider a class $\Omega$ given by \begin{equation}\label{omega}\Omega=\left\{f\in\mathcal{A}\colon<span class="Apple-converted-space"> </span><span class="Apple-converted-space"> </span>|zf'(z)-f(z)|<\frac{1}{2},\ z\in\mathbb{D}\right\}.\tag{0.2}\end{equation} For these two classes, we establish inclusion relations involving some well-known subclasses of $\mathcal{S}^*$ and compute radius estimates featuring various pairings of these classes.</p>S. Sivaprasad KumarPriyanka Priyanka
Copyright (c) 2024 Priyanka Goel, S. Sivaprasad Kumar
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2024-03-252024-03-2576340542210.3842/umzh.v76i3.7317Laguerre–Cayley functions and related polynomials
https://umj.imath.kiev.ua/index.php/umj/article/view/7810
<p>UDC 517.587</p> <p>We investigate the main properties of Laguerre–Cayley functions and related polynomials, which can be regarded as an essential component of<span class="Apple-converted-space"> </span>mathematical apparatus of the functional-discrete (FD-) method for solving the Cauchy problem for an abstract homogeneous evolutionary equation of<span class="Apple-converted-space"> </span>fractional order.</p>V. MakarovS. Makarov
Copyright (c) 2024 Володимир Леонідович Макаров
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2024-03-252024-03-2576342343110.3842/umzh.v76i3.7810Some new Cesàro sequence spaces of order $\alpha$
https://umj.imath.kiev.ua/index.php/umj/article/view/7333
<p>UDC 517.98</p> <p>We introduce the spaces $\ell_\infty(C_\alpha),$ $f(C_\alpha),$ and $f_0(C_\alpha)$ of Ces\`{a}ro bounded, Ces\`{a}ro almost convergent, and Ces\`{a}ro almost null sequences of order $\alpha,$ respectively. Moreover, we establish some inclusion relations for these spaces and determine the $\alpha$-, $\beta$- and $\gamma$-duals of the spaces<span class="Apple-converted-space"> </span>$\ell_\infty(C_\alpha)$ and $f(C_\alpha).$<span class="Apple-converted-space"> </span>Finally, we characterize the classes of matrix transformations from the space $f(C_\alpha)$ to any sequence space $Y$ and from any sequence space $Y$ to the space $f(C_\alpha).$</p>Medine Yeşilkayagil SavaşcıFeyzi Başar
Copyright (c) 2024 Feyzi Başar
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2024-03-252024-03-2576343244610.3842/umzh.v76i3.7333Rotational interval exchange transformations
https://umj.imath.kiev.ua/index.php/umj/article/view/7779
<p>UDC 517.5</p> <p>We show the equivalence of two possible definitions of a rotational interval exchange transformation: by the first definition, it is the first return map for a circle rotation onto a union of finitely many circle arcs and, by the second definition, it is an interval exchange with a scheme (in the sense of interval rearrangement ensembles) whose dual is also an interval exchange scheme.</p>A. Teplinsky
Copyright (c) 2024 Олексій Теплінський
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2024-03-252024-03-2576344746710.3842/umzh.v76i3.7779On continuous extension to the boundary of a domain of the Cauchy-type integral with parameter-dependent density
https://umj.imath.kiev.ua/index.php/umj/article/view/7849
<p>UDC 517.54</p> <p>We establish sufficient conditions for the continuous extension of a Cauchy-type integral whose density depends on the parameter to<span class="Apple-converted-space"> </span>a nonsmooth integration line.</p>S. Plaksa
Copyright (c) 2024 Сергій Анатолійович Плакса
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2024-03-252024-03-2576346847210.3842/umzh.v76i3.7849