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 2022, the journal was included to Scopus.</p><p><em>Attention:</em> The template of the submission (.tex and .cls files) was updated on 03.01.2023. 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.)Sat, 31 Dec 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/389
Editors Editors
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https://vestnmath.dnu.dp.ua/index.php/rim/article/view/389Sat, 31 Dec 2022 00:00:00 +0000Additional Fibonacci-Bernoulli relations
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/390
We continue our study on relationships between Fibonacci (Lucas) numbers and Bernoulli numbers and polynomials. The derivations of our results are based on functional equations for the respective generating functions, which in our case are combinations of hyperbolic functions. Special cases and some corollaries will highlight interesting aspects of our findings.K. Adegoke, R. Frontczak, T.P. Goy
Copyright (c) 2022 K. Adegoke, R. Frontczak, T.P. Goy
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https://vestnmath.dnu.dp.ua/index.php/rim/article/view/390Sat, 31 Dec 2022 00:00:00 +0000A Lambda Analogue of the Gamma Function and its Properties
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/391
We consider a generalization of the gamma function which we term as lambda analogue of the gamma function or $$$\lambda$$$-gamma function and further, we establish some of its accompanying properties. For the particular case when $$$\lambda=1$$$, the results established reduce to results involving the classical gamma function. The techniques employed in proving our results are analytical in nature.K. Nantomah, I. Ege
Copyright (c) 2022 K. Nantomah, I. Ege
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https://vestnmath.dnu.dp.ua/index.php/rim/article/view/391Sat, 31 Dec 2022 00:00:00 +0000The homology groups $$$H_{n+1} \left( \mathbb{C}\Omega_n \right)$$$
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/392
<p>The topic of the paper is the investigation of the homology groups of the $$$(2n+1)$$$-dimensional CW-complex $$$\mathbb{C}\Omega_n$$$. The spaces $$$\mathbb{C}\Omega_n$$$ consist of complex-valued functions and are the analogue of the spaces $$$\Omega_n$$$, widely known in the approximation theory. The spaces $$$\mathbb{C}\Omega_n$$$ have been introduced in 2015 by A.M. Pasko who has built the CW-structure of the spaces $$$\mathbb{C}\Omega_n$$$ and using this CW-structure established that the spaces $$$\mathbb{C}\Omega_n$$$ are simply connected. Note that the mentioned CW-structure of the spaces $$$\mathbb{C}\Omega_n$$$ is the analogue of the CW-structure of the spaces $$$\Omega_n$$$ constructed by V.I. Ruban. Further A.M. Pasko found the homology groups of the space $$$\mathbb{C}\Omega_n$$$ in the dimensionalities $$$0, 1, \ldots, n, 2n-1, 2n, 2n+1$$$. The goal of the present paper is to find the homology group $$$H_{n+1}\left ( \mathbb{C}\Omega_n \right )$$$. It is proved that $$$H_{n+1} \left ( \mathbb{C}\Omega_n \right )=\mathbb{Z}^\frac{n+1}{2}$$$ if $$$n$$$ is odd and $$$H_{n+1} \left ( \mathbb{C}\Omega_n \right )=\mathbb{Z}^\frac{n+2}{2}$$$ if $$$n$$$ is even.</p>A.M. Pasko
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https://vestnmath.dnu.dp.ua/index.php/rim/article/view/392Sat, 31 Dec 2022 00:00:00 +0000Characterization of Biharmonic Hypersurface
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/393
The main purpose of this paper is to study biharmonic hypersurface in a quasi-paraSasakian manifold $$$\mathbb{Q}^{2m+1}$$$. Biharmonic hypersurfaces are special cases of biharmonic maps and biharmonic maps are the critical points of the bienergy functional. The condition of biharmonicity for non-degenerate hypersurfaces in $$$\mathbb{Q}^{2m+1}$$$ is investigated for both cases: either the characteristic vector field of $$$\mathbb{Q}^{2m+1}$$$ is the unit normal vector field to the hypersurface or it belongs to the tangent space of the hypersurface. Some relevant examples are also illustrated.S.K. Srivastava, K. Sood, K. Srivastava
Copyright (c) 2022 S.K. Srivastava, K. Sood, K. Srivastava
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https://vestnmath.dnu.dp.ua/index.php/rim/article/view/393Sat, 31 Dec 2022 00:00:00 +0000