Acta et Commentationes Universitatis Tartuensis de Mathematica <p><em>Acta et Commentationes Universitatis Tartuensis de Mathematica&nbsp;</em>(ACUTM) is an international journal of pure and applied mathematics.</p> University of Tartu Press en-US Acta et Commentationes Universitatis Tartuensis de Mathematica 1406-2283 On the uniqueness of two different classes of meromorphic functions under the sharing of two sets of rational functions <p>We study the uniqueness problem of two special classes of meromorphic functions sharing two sets of small functions. One of the considered classes has the property to include the Selberg class <em>L</em> functions, while the other class is comprising of arbitrary meromorphic functions having finitely many poles. We obtain a number of results which extend and improve a number of earlier results such as Li [ Proc. Amer. Math. Soc., <strong>138</strong> (2010), 2071-2077], Lin and Lin [Filomat <strong>30</strong> (2016), 3795-3806] and others. We have also been able to replace the strict CM (IM) sharing of the sets in our theorems to almost CM (almost IM) sharing.&nbsp;</p> Abhijit Banerjee Arpita Kundu Copyright (c) 2022-05-27 2022-05-27 26 1 5 23 10.12697/ACUTM.2022.26.01 Coefficients bounds for a family of bi-univalent functions defined by Horadam polynomials <p>In the present paper, we determine upper bounds for the first two Taylor–Maclaurin coefficients |a2| and |a3| for a certain family of holomorphic and bi-univalent functions defined by using the Horadam polynomials. Also, we solve Fekete–Szegö problem of functions belonging to this family. Further, we point out several special cases of our results.</p> Abbas Kareem Wanas Basem A. Frasin Sondekola R. Swamy Yerragunta Sailaja Copyright (c) 2022-05-28 2022-05-28 26 1 25 32 10.12697/ACUTM.2022.26.02 On the bicomplex Gaussian Fibonacci and Gaussian Lucas numbers <p>We give the bicomplex Gaussian Fibonacci and the bicomplex Gaussian Lucas numbers and establish the generating functions and Binet’s formulas related to these numbers. Also, we present the summation formula, matrix representation and Honsberger identity and their relationship between these numbers. Finally, we show the relationships among the bicomplex Gaussian Fibonacci, the bicomplex Gaussian Lucas, Gaussian Fibonacci, Gaussian Lucas and Fibonacci numbers.</p> Engin Özkan Bahar Kuloğlu Copyright (c) 2022-05-28 2022-05-28 26 1 33 43 10.12697/ACUTM.2022.26.03 Fekete's lemma for componentwise subadditive functions of two or more real variables <p>We prove an analogue of Fekete's subadditivity lemma for functions of several real variables which are subadditive in each variable taken singularly. This extends both the classical case for subadditive functions of one real variable, and a similar result for functions of integer variables. While doing so, we prove that the functions with the property mentioned above are bounded in every closed and bounded subset of their domain. The arguments expand on those in Chapter 6 of E. Hille's 1948 textbook.</p> Silvio Capobianco Copyright (c) 2022-05-29 2022-05-29 26 1 45 62 10.12697/ACUTM.2022.26.04 Natural vibrations of curved nano-beams and nano-arches <p>The natural vibrations of curved nano-beams and nano-arches are studied. The nano-arches under consideration have piecewise constant thickness; these are weakened with stable cracks located at re-entrant corners of the steps. A method of determination of natural frequencies is developed making use of the method of weightless rotating spring. The aim of the paper is to assess the sensitivity of the eigenfrequencies on the geometrical and physical parameters of the nano-arch. The results of the calculations favourably compare with similar works of other researchers.</p> Shahid Mubasshar Jaan Lellep Copyright (c) 2022-05-29 2022-05-29 26 1 63 76 10.12697/ACUTM.2022.26.05 The Sasaki-Kenmotsu manifolds <p>In the present paper, we introduce a new class of structures on an even dimensional differentiable Riemannian manifold which combines, well known in literature, the Sasakian and Kenmotsu structures simultaneously. The structure will be called a Sasaki–Kenmotsu structure by us. Firstly, we discuss the normality of the Sasaki–Kenmotsu structure and give some basic properties. Secondly, we present some important results concerning with the curvatures of the Sasaki–Kenmotsu manifold. Finally, we show the existence of the Sasaki–Kenmotsu structure by giving some concrete examples.</p> Aydin Gezer Gherici Beldjilali Copyright (c) 2022-05-29 2022-05-29 26 1 77 88 10.12697/ACUTM.2022.26.06 Two new examples of Banach spaces with a plastic unit ball <p>We prove that Banach spaces ℓ<sub>1</sub> ⊕<sub>2</sub> R and <em>X</em> ⊕<sub>∞</sub> <em>Y</em> , with strictly convex <em>X</em> and <em>Y</em> , have plastic unit balls (we call a metric space plastic if every non-expansive bijection from this space onto itself is an isometry).</p> Olesia Zavarzina Nikita Leo Rainis Haller Copyright (c) 2022-05-29 2022-05-29 26 1 89 101 10.12697/ACUTM.2022.26.07 Current Hom-Lie algebras <p>In this paper, we study Hom-Lie structures on tensor products. In particular, we consider current Hom-Lie algebras and discuss their representations. We determine faithful representations of minimal dimension of current Heisenberg Hom-Lie algebras. Moreover derivations, including generalized derivations, and centroids are studied. Furthermore, cohomology and extensions of current Hom-Lie algebras are also considered.</p> Torkia Ben Jmaa Abdenacer Makhlouf Nejib Saadaoui Copyright (c) 2022-05-30 2022-05-30 26 1 103 127 10.12697/ACUTM.2022.26.08 Diophantine equations involving the bi-periodic Fibonacci and Lucas sequences <p>In this paper, we present new identities involving the biperiodic Fibonacci and Lucas sequences. Then we solve completely some quadratic Diophantine equations involving the bi-periodic Fibonacci and Lucas sequences.</p> Lyes AIT-AMRANE Djilali BEHLOUL Akila DJOUMAKH Copyright (c) 2022-05-30 2022-05-30 26 1 129 152 10.12697/ACUTM.2022.26.09 About the transitivity of the property of being Segal topological algebra <p>We show that if (A, f, B) and (B, g, C) are left (right or two-sided) Segal topological algebras for which g(f(A))⊆ g(B)g(f(A))&nbsp; (g(f(A))⊆ g(f(A))g(B)&nbsp; or&nbsp; g(f(A))⊆ g(B)g(f(A))∩ g(f(A))g(B), respectively), then (A, g∘ f, C) is also a left (right or two-sided, respectively) Segal topological algebra.</p> Mart Abel Copyright (c) 2022-05-27 2022-05-27 26 1 153 160 10.12697/ACUTM.2022.26.10 Central part interpolation schemes for a class of fractional initial value problems <p>We consider an initial value problem for linear fractional integro-differential equations with weakly singular kernels. Using an integral equation reformulation of the underlying problem, a collocation method based on the central part interpolation by continuous piecewise polynomials on the uniform grid is constructed and analysed. Optimal convergence order of the proposed method is established and confirmed by numerical experiments.</p> Mikk Vikerpuur Margus Lillemäe Arvet Pedas Copyright (c) 2022-05-27 2022-05-27 26 1 161 178 10.12697/ACUTM.2022.26.11