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 Comparison of estimators of variance parameters in the growth curve model with a special variance structure <p>Three different estimators of the variance parameters in the growth curve model with generalized uniform correlation structure are compared on the basis of mean square error. Since the situation in general depends on specific choice of the structure matrix, we investigate two important special cases.</p> Rastislav Rusnačko Ivan Žežula ##submission.copyrightStatement## 2017-12-01 2017-12-01 21 2 171 184 10.12697/ACUTM.2017.21.11 Coefficient inequality for transforms of certain subclass of analytic functions <p>The objective of this paper is to obtain the best possible sharp upper bound for the second Hankel functional associated with the <em>k<sup>th</sup></em> root transform [<em>f</em>(<em>z<sup>k</sup></em>)]<sup>1/<em>k</em></sup> of normalized analytic function <em>f(z)</em> when it belongs to certain subclass of analytic functions, defined on the open unit disc in the complex plane using Toeplitz determinants.</p> T. RamReddy D. Shalini D. Vamshee Krishna B. Venkateswarlu ##submission.copyrightStatement## 2017-12-01 2017-12-01 21 2 185 193 10.12697/ACUTM.2017.21.12 A note on a new unique range set with truncated multiplicity <p>We introduce a new polynomial whose zero set forms a unique range set for meromorphic function with 11 elements under relaxed sharing hypothesis.</p> Abhijit Banerjee Santanu Dhar ##submission.copyrightStatement## 2017-12-22 2017-12-22 21 2 195 205 10.12697/ACUTM.2017.21.13 Tests of exponentiality against some parametric over/under-dispersed life time models <p>We develop tests of goodness of fit of the exponential model against some over/under dispersion family of distributions. In particular, we develop 3 score test statistics and 3 likelihood ratio statistics. These are (<em>S</em><sub>1</sub>, <em>L</em><sub>1</sub>), (<em>S</em><sub>2</sub>, <em>L</em><sub>2</sub>), and (<em>S</em><sub>3</sub>, <em>L</em><sub>3</sub>) based on a general over-dispersed family of distributions, two specic over/under dispersed exponential models, namely, the gamma and the Weibull distributions, respectively. A simulation study shows that the statistics <em>S</em><sub>3</sub> and <em>L</em><sub>3</sub> have best overall performance, in terms of both, level and power. However, the statistic <em>L</em><sub>3</sub> can be liberal in some instances and it needs the maximum likelihood estimates of the parameters of the Weibull distribution as opposed to the statistic <em>S</em><sub>3</sub> which is very simple to use. So, our recommendation is to use the statistic <em>S</em><sub>3</sub> to test the fit of an exponential distribution over any over/under-dispersed exponential distribution.</p> Rajibul Mian Sudhir Paul ##submission.copyrightStatement## 2017-12-22 2017-12-22 21 2 207 223 10.12697/ACUTM.2017.21.14 Uncertain fuzzy Ostrowski type inequalities for the generalized (s,m)-preinvex Godunova-Levin functions of second kind <p>In the present paper, the notion of the generalized (<em>s, m</em>)- preinvex Godunova-Levin function of second kind is introduced and some uncertain fuzzy Ostrowski type inequalities for the generalized (<em>s, m</em>)-preinvex Godunova-Levin functions of second kind via classical integrals and Riemann-Liouville fractional integrals are established.</p> Artion Kashuri Rozana Liko ##submission.copyrightStatement## 2017-12-22 2017-12-22 21 2 225 238 10.12697/ACUTM.2017.21.15 Coincidence of topological Jacobson radicals in topological algebras <p>Several classes of topological algebras for which the left topological Jacobson radical coincides with the right topological Jacobson radical are described.</p> Mart Abel Mati Abel Paul Tammo ##submission.copyrightStatement## 2017-12-22 2017-12-22 21 2 239 247 10.12697/ACUTM.2017.21.16 On basicity of the degenerate trigonometric system with excess <p>The basis properties (completeness, minimality and Schauder basicity) of systems of the form {<em>ω</em>(<em>t</em>)<em>φ</em><sub><em>n</em></sub>(<em>t</em>)}, where {<em>φ</em><sub><em>n</em></sub>(<em>t</em>)} is an exponential or trigonometric (cosine or sine) systems, have been investigated in several papers. Concrete examples of the weight function <em>ω</em>(<em>t</em>) are known for which the system itself is not complete and minimal but has excess – becomes complete and minimal in corresponding <em>L<sub>p</sub></em> space only after elimination of some of its elements. The aim of this paper is to show that if <em>ω</em>(<em>t</em>) is any measurable weight function such that the system {<em>ω</em>(<em>t</em>) sin <em>nt</em>}<sub><em>n</em>∊ℕ</sub> has excess, then neither this system itself, nor a system obtained from it by elimination of an element, is not a Schauder basis.</p> Aydin Sh. Shukurov ##submission.copyrightStatement## 2017-12-22 2017-12-22 21 2 249 257 10.12697/ACUTM.2017.21.17 On the properties of k-balancing and k-Lucas-balancing numbers <p>The <em>k</em>-Lucas-balancing numbers are obtained from a special sequence of squares of <em>k</em>-balancing numbers in a natural form. In this paper, we will study some properties of <em>k</em>-Lucas-balancing numbers and establish relationship between these numbers and <em>k</em>-balancing numbers.</p> Prasanta Kumar Ray ##submission.copyrightStatement## 2017-12-22 2017-12-22 21 2 259 274 10.12697/ACUTM.2017.21.18 On Salagean type pseudo-starlike functions <p>We construct two new subclasses of univalent functions in the open unit disk <em>U</em> = {<em>z</em> : |<em>z</em>| &lt; 1}. For the first class <em>£<sub>λ</sub></em>(<em>β</em>) of Salagean type <em>λ</em>-pseudo-starlike functions, using the sigmoid function, we establish upper bounds for the initial coefficients of the functions in this class. Furthermore, for the second class <em>£<sub>λ</sub></em> (<em>β</em>, <em>φ</em>) we obtain Fekete-Szegö inequalities. The results presented in this paper generalize the recent work of Babalola.</p> Şahsene Altınkaya Yeşim Sağlam Özkan ##submission.copyrightStatement## 2017-12-22 2017-12-22 21 2 275 285 10.12697/ACUTM.2017.21.19 Some inequalities associated with the Hermite-Hadamard inequalities for operator h-convex functions <p>We introduce the concept of operator <em>h</em>-convex functions for positive linear maps, and prove some Hermite-Hadamard type inequalities for these functions. As applications, we obtain several trace inequalities for operators.</p> V. Darvish S. S. Dragomir H. M. Nazari A. Taghavi ##submission.copyrightStatement## 2017-12-22 2017-12-22 21 2 287.297 287.297 10.12697/ACUTM.2017.21.20