Acta et Commentationes Universitatis Tartuensis de Mathematica
http://acutm.math.ut.ee/index.php/acutm
<p><em>Acta et Commentationes Universitatis Tartuensis de Mathematica </em>(ACUTM) is an international journal of pure and applied mathematics.</p>University of Tartu Pressen-USActa et Commentationes Universitatis Tartuensis de Mathematica1406-2283On Jordan's and Kober's inequality
http://acutm.math.ut.ee/index.php/acutm/article/view/ACUTM.2016.20.09
We refine some classical inequalities for trigonometric functions, such as Jordan's inequality, Cusa–Huygens's inequality, and Kober's inequality.Barkat Ali BhayoJózsef Sándor2016-12-022016-12-02202New iteration process for a general class of contractive mappings
http://acutm.math.ut.ee/index.php/acutm/article/view/ACUTM.2016.20.10
Let <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.Adesanmi Alao Mogbademu2016-12-022016-12-02202On translation surfaces in 4-dimensional Euclidean space
http://acutm.math.ut.ee/index.php/acutm/article/view/ACUTM.2016.20.11
We 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.Kadri ArslanBengü BayramBetül BulcaGünay Öztürk2016-12-022016-12-02202Results on the number of zeros in a disk for three types of polynomials
http://acutm.math.ut.ee/index.php/acutm/article/view/ACUTM.2016.20.12
See PDF.Derek BryantRobert Gardner2016-12-022016-12-02202On φ-pseudo symmetric LP-Sasakian manifolds with respect to quarter-symmetric non-metric connections
http://acutm.math.ut.ee/index.php/acutm/article/view/ACUTM.2016.20.13
The 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.Santu DeyArindam Bhattacharyya2016-12-022016-12-02202Certain Diophantine equations involving balancing and Lucas-balancing numbers
http://acutm.math.ut.ee/index.php/acutm/article/view/ACUTM.2016.20.14
It 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.Prasanta Kumar Ray2016-12-022016-12-02202