http://acutm.math.ut.ee/index.php/acutm/issue/feedActa et Commentationes Universitatis Tartuensis de Mathematica2016-12-02T21:16:14+02:00Enno Kolkenno.kolk@ut.eeOpen Journal Systems<p><em>Acta et Commentationes Universitatis Tartuensis de Mathematica </em>(ACUTM) is an international journal of pure and applied mathematics.</p>http://acutm.math.ut.ee/index.php/acutm/article/view/ACUTM.2016.20.09On Jordan's and Kober's inequality2016-12-02T21:16:14+02:00Barkat Ali Bhayobhayo.barkat@gmail.comJózsef Sándorjsandor@math.ubbcluj.roWe refine some classical inequalities for trigonometric functions, such as Jordan's inequality, Cusa–Huygens's inequality, and Kober's inequality.2016-12-02T00:00:00+02:00http://acutm.math.ut.ee/index.php/acutm/article/view/ACUTM.2016.20.10New iteration process for a general class of contractive mappings2016-12-02T21:16:14+02:00Adesanmi Alao Mogbademuamogbademu@unilag.edu.ngLet <em>K</em> be a closed convex subset of <em>X</em>, and let <em>T</em> : <em>K</em> → <em>K</em> be a self-mapping with the set <em>F<sub>T</sub></em> of fixed points such that ‖<em>Tx</em> − <em>ρ</em>‖ ≤ <em>δ</em>‖<em>x</em> − <em>ρ</em>‖ for all <em>x</em> ∈ <em>K</em>, <em>ρ</em> ∈ <em>F<sub>T</sub></em> and some <em>δ</em> ∈ (0, 1). We introduce a new iteration process called Picard-hybrid iteration and show that this iteration process converges to the unique fixed point of <em>T</em>. It is also shown that our iteration process converges more rapidly than the Picard–Mann and Picard iteration processes. Our result improves a recent result of S. H. Khan and some other results.2016-12-02T00:00:00+02:00http://acutm.math.ut.ee/index.php/acutm/article/view/ACUTM.2016.20.11On translation surfaces in 4-dimensional Euclidean space2016-12-02T21:16:14+02:00Kadri Arslanarslan@uludag.edu.trBengü Bayrambenguk@balikesir.edu.trBetül Bulcabbulca@uludag.edu.trGünay Öztürkogunay@kocaeli.edu.trWe consider translation surfaces in Euclidean spaces. Firstly, we give some results of translation surfaces in the 3-dimensional Euclidean space E<sup>3</sup>. Further, we consider translation surfaces in the 4-dimensional Euclidean space E<sup>4</sup>. We prove that a translation surface is flat in E<sup>4</sup> if and only if it is either a hyperplane or a hypercylinder. Finally we give necessary and sufficient condition for a quadratic triangular Bézier surface in E<sup>4</sup> to become a translation surface.2016-12-02T00:00:00+02:00http://acutm.math.ut.ee/index.php/acutm/article/view/ACUTM.2016.20.12Results on the number of zeros in a disk for three types of polynomials2016-12-02T21:16:14+02:00Derek Bryanttyk@ut.eeRobert Gardnergardnerr@etsu.eduSee PDF.2016-12-02T00:00:00+02:00http://acutm.math.ut.ee/index.php/acutm/article/view/ACUTM.2016.20.13On φ-pseudo symmetric LP-Sasakian manifolds with respect to quarter-symmetric non-metric connections2016-12-02T21:16:14+02:00Santu Deysantu.mathju@gmail.comArindam Bhattacharyyabhattachar1968@yahoo.co.inThe object of the present paper is to study <em>φ</em>-pseudo symmetric and <em>φ</em>-pseudo Ricci symmetric LP-Sasakian manifolds with respect to Levi–Civita connections and quarter-symmetric non-metric connections. We obtain a necessary and sufficient condition for a <em>φ</em>-pseudo symmetric LP-Sasakian manifold with respect to a quarter symmetric non-metric connection to be <em>φ</em>-pseudo symmetric LP-Sasakian manifold with respect to a Levi–Civita connection.2016-12-02T00:00:00+02:00http://acutm.math.ut.ee/index.php/acutm/article/view/ACUTM.2016.20.14Certain Diophantine equations involving balancing and Lucas-balancing numbers2016-12-02T21:16:14+02:00Prasanta Kumar Rayrayprasanta2008@gmail.comIt is well known that if <em>x</em> is a balancing number, then the positive square root of 8<em>x</em><sup>2</sup> + 1 is a Lucas-balancing number. Thus, the totality of balancing number <em>x</em> and Lucas-balancing number <em>y</em> are seen to be the positive integral solutions of the Diophantine equation 8<em>x</em><sup>2</sup> +1 = <em>y</em>2. In this article, we consider some Diophantine equations involving balancing and Lucas-balancing numbers and study their solutions.2016-12-02T00:00:00+02:00