Researches in Mathematics
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<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 publishes, semiannually, research articles in basic areas of theoretical and applied mathematics, including, but not limited to: analysis, algebra, geometry, topology, probability theory and mathematical statistics, differential equations and mathematical physics.</p><p>The journal was published annually from 1963 to 1997 under the title “Researches on modern problems of summation and approximation of functions and their applications” and from 1998 to 2018 under the title “Dnipro University Mathematics Bulletin”.</p><p>In January 2022, the journal was accepted and now is in the process of being added to Scopus.</p><p><em>Attention:</em> The template of the submission (.tex and .cls files) was updated on 20.03.2022. Please proceed to <a href="/index.php/rim/about/submissions#authorGuidelines">Author Guidelines</a> to download and use the latest version.</p></td></tr></tbody></table>en-USAuthors 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>vestmath@mmf.dnu.edu.ua (Editorial Mediator)dnuvestmath@gmail.com (Honcharov S.V.)Mon, 04 Jul 2022 00:00:00 +0000OJS 2.4.8.0http://blogs.law.harvard.edu/tech/rss60Preamble
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/381
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https://vestnmath.dnu.dp.ua/index.php/rim/article/view/381Mon, 04 Jul 2022 12:19:27 +0000General form of $$$(\lambda,\varphi)$$$-additive operators on spaces of $$$L$$$-space-valued functions
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/382
The goal of the article is to characterize continuous $$$(\lambda,\varphi)$$$-additive operators acting on measurable bounded functions with values in $$$L$$$-spaces. As an application, we prove a sharp Ostrowski type inequality for such operators.V.F. Babenko, V.V. Babenko, O.V. Kovalenko, N.V. Parfinovych
Copyright (c) 2022 V.F. Babenko, V.V. Babenko, O.V. Kovalenko, N.V. Parfinovych
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https://vestnmath.dnu.dp.ua/index.php/rim/article/view/382Mon, 04 Jul 2022 12:19:27 +0000Solitary and periodic wave solutions of the loaded modified Benjamin-Bona-Mahony equation via the functional variable method
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/383
In this article, we established new travelling wave solutions for the loaded Benjamin-Bona-Mahony and the loaded modified Benjamin-Bona-Mahony equation by the functional variable method. The performance of this method is reliable and effective and gives the exact solitary wave solutions and periodic wave solutions. All solutions of these equations have been examined and three dimensional graphics of the obtained solutions have been drawn by using the Matlab program. We get some traveling wave solutions, which are expressed by the hyperbolic functions and trigonometric functions. This method is effective to find exact solutions of many other similar equations.B. Babajanov, F. Abdikarimov
Copyright (c) 2022 B. Babajanov, F. Abdikarimov
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https://vestnmath.dnu.dp.ua/index.php/rim/article/view/383Mon, 04 Jul 2022 12:19:27 +0000Three- and four-term recurrence relations for Horn's hypergeometric function $$$H_4$$$
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/384
Three- and four-term recurrence relations for hypergeometric functions of the second order (such as hypergeometric functions of Appell, Horn, etc.) are the starting point for constructing branched continued fraction expansions of the ratios of these functions. These relations are essential for obtaining the simplest structure of branched continued fractions (elements of which are simple polynomials) for approximating the solutions of the systems of partial differential equations, as well as some analytical functions of two variables. In this study, three- and four-term recurrence relations for Horn's hypergeometric function $$$H_4$$$ are derived. These relations can be used to construct branched continued fraction expansions for the ratios of this function and they are a generalization of the classical three-term recurrent relations for Gaussian hypergeometric function underlying Gauss' continued fraction.R.I. Dmytryshyn, I.-A.V. Lutsiv
Copyright (c) 2022 R.I. Dmytryshyn, I.-A.V. Lutsiv
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https://vestnmath.dnu.dp.ua/index.php/rim/article/view/384Mon, 04 Jul 2022 12:19:28 +0000Strengthening the Comparison Theorem and Kolmogorov Inequality in the Asymmetric Case
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/385
<p>We obtain the strengthened Kolmogorov comparison theorem in asymmetric case.<br />In particular, it gives us the opportunity to obtain the following strengthened Kolmogorov inequality in the asymmetric case:<br />$$<br />\|x^{(k)}_{\pm }\|_{\infty}\le \frac<br />{\|\varphi _{r-k}( \cdot \;;\alpha ,\beta )_\pm \|_{\infty }}<br />{E_0(\varphi _r( \cdot \;;\alpha ,\beta ))^{1-k/r}_{\infty }}<br />|||x|||^{1-k/r}_{\infty}<br />\|\alpha^{-1}x_+^{(r)}+\beta^{-1}x_-^{(r)}\|_\infty^{k/r}<br />$$<br />for functions $$$x \in L^r_{\infty }(\mathbb{R})$$$, where<br />$$<br />|||x|||_\infty:=\frac12 \sup_{\alpha ,\beta}\{ |x(\beta)-x(\alpha)|:x'(t)\neq 0 \;\;\forall<br />t\in (\alpha ,\beta) \}<br />$$<br />$$$k,r \in \mathbb{N}$$$, $$$k<r$$$, $$$\alpha, \beta > 0$$$, $$$\varphi_r( \cdot \;;\alpha ,\beta )_r$$$ is the asymmetric perfect spline of Euler of order $$$r$$$ and $$$E_0(x)_\infty $$$ is the best uniform approximation of the function $$$x$$$ by constants.</p>V.A. Kofanov, K.D. Sydorovych
Copyright (c) 2022 V.A. Kofanov, K.D. Sydorovych
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https://vestnmath.dnu.dp.ua/index.php/rim/article/view/385Mon, 04 Jul 2022 12:19:29 +0000A parametric type of Bernoulli polynomials with higher level
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/386
In this paper, we introduce a parametric type of Bernoulli polynomials with higher level and study their characteristic and combinatorial properties. We also give determinant expressions of a parametric type of Bernoulli polynomials with higher level. The results are generalizations of those with level 2 by Masjed-Jamei, Beyki and Koepf and with level 3 by the author.T. Komatsu
Copyright (c) 2022 T. Komatsu
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https://vestnmath.dnu.dp.ua/index.php/rim/article/view/386Mon, 04 Jul 2022 12:19:29 +0000Two sharp inequalities for operators in a Hilbert space
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/387
In this paper we obtained generalisations of the L. V. Taikov’s and N. Ainulloev’s sharp inequalities, which estimate a norm of function's first-order derivative (L. V. Taikov) and a norm of function's second-order derivative (N. Ainulloev) via the modulus of continuity or the modulus of smoothness of the function itself and the modulus of continuity or the modulus of smoothness of the function's second-order derivative. The generalisations are obtained on the power of unbounded self-adjoint operators which act in a Hilbert space. The moduli of continuity or smoothness are defined by a strongly continuous group of unitary operators.N.O. Kriachko
Copyright (c) 2022 N.O. Kriachko
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https://vestnmath.dnu.dp.ua/index.php/rim/article/view/387Mon, 04 Jul 2022 12:19:29 +0000The fundamental group of the space $$$\Omega_n(m)$$$
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/388
In the present paper the spaces $$$\Omega_n(m)$$$ are considered. The spaces $$$\Omega_n(m)$$$, introduced in 2018 by A.M. Pasko and Y.O. Orekhova, are the generalization of the spaces $$$\Omega_n$$$ (the space $$$\Omega_n(2)$$$ coincides with $$$\Omega_n$$$). The investigation of homotopy properties of the spaces $$$\Omega_n$$$ has been started by V.I. Ruban in 1985 and followed by V.A. Koshcheev, A.M. Pasko. In particular V.A. Koshcheev has proved that the spaces $$$\Omega_n$$$ are simply connected. We generalized this result proving that all the spaces $$$\Omega_n(m)$$$ are simply connected. In order to prove the simply connectedness of the space $$$\Omega_n(m)$$$ we consider the 1-skeleton of this space. Using 1-cells we form the closed ways that create the fundamental group of the space $$$\Omega_n(m)$$$. Using 2-cells we show that all these closed ways are equivalent to the trivial way. So the fundamental group of the space $$$\Omega_n(m)$$$ is trivial and the space $$$\Omega_n(m)$$$ is simply connected.A.M. Pasko
Copyright (c) 2022 A.M. Pasko
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https://vestnmath.dnu.dp.ua/index.php/rim/article/view/388Mon, 04 Jul 2022 12:19:30 +0000