CUBO, A Mathematical Journal http://revistas.ufro.cl/ojs/index.php/cubo <p align="justify">CUBO, A Mathematical Journal is a scientific journal founded in 1985 by the Universidad de La Frontera, Temuco - Chile. The journal publishes original papers containing substantial results in areas of pure and applied mathematics. CUBO appears in three issues per year and is indexed in ZentralBlatt Math., Mathematical Reviews, MathSciNet, Latin Index and SciELO-Chile.</p> Universidad de La Frontera. Temuco, Chile. en-US CUBO, A Mathematical Journal 0716-7776 Caputo fractional Iyengar type Inequalities http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2153 <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>Here we present Caputo fractional Iyengar type inequalities with respect to Lp norms, with 1 ≤ p ≤ ∞. The method is based on the right and left Caputo fractional Taylor’s formulae.</p> </div> </div> </div> George A. Anastassiou Copyright (c) 2019 CUBO, A Mathematical Journal 2019-08-10 2019-08-10 21 2 01–13 01–13 10.4067/S0719-06462019000200001 Zk-Magic Labeling of Path Union of Graphs http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2154 <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>For any non-trivial Abelian group A under addition a graph <em>G</em> is said to be <em>A-magic</em> if there exists a labeling <em>f : E(G) → A</em> − {0} such that, the vertex labeling <em>f</em><sup>+</sup> defined as <em>f</em><sup>+</sup>(<em>v</em>) = ∑<em>f</em>(<em>uv</em>) taken over all edges <em>uv</em> incident at <em>v</em> is a constant. An <em>A-magic</em> graph <em>G</em> is said to be <em>Z<sub>k</sub></em>-<em>magic</em> graph if the group <em>A</em> is <em>Z<sub>k</sub></em>, the group of integers modulo <em>k</em> and these graphs are referred as <em>k-magic</em> graphs. In this paper we prove that the graphs such as path union of cycle, generalized Petersen graph, shell, wheel, closed helm, double wheel, flower, cylinder, total graph of a path, lotus inside a circle and <em>n</em>-pan graph are <em>Z<sub>k</sub>-magic</em> graphs.</p> </div> </div> </div> P. Jeyanthi K. Jeya Daisy Andrea Semaničová-feňovčíková Copyright (c) 2019 CUBO, A Mathematical Journal 2019-08-10 2019-08-10 21 2 15–40 15–40 10.4067/S0719-06462019000200015 Totally umbilical proper slant submanifolds of para-Kenmotsu manifold http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2155 <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>In this paper, we study slant submanifolds of a para-Kenmotsu manifold. We prove that totally umbilical slant submanifold of a para-Kenmotsu manifold is either invariant or anti-invariant or dimension of submanifold is 1 or the mean curvature vector H of the submanifold lies in the invariant normal subbundle.</p> </div> </div> </div> M.S. Siddesha C.S. Bagewadi D. Nirmala Copyright (c) 2019-08-10 2019-08-10 21 2 41–49 41–49 10.4067/S0719-06462019000200041 The perimeter of a flattened ellipse can be estimated accurately even from Maclaurin’s series http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2158 <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>For the perimeter <em>P</em> (<em>a, b</em>) of an ellipse with the semi-axes <em>a</em> ≥ <em>b</em> ≥ 0 a sequence <em>Q<sub>n</sub></em>(<em>a, b</em>) is constructed such that the relative error of the approximation <em>P</em>(<em>a,b</em>) ≈ <em>Q<sub>n</sub></em>(<em>a,b</em>) satisfies the following inequalities</p> <p>0 ≤ −(<em>P</em>(<em>a,b</em>)−<em>Q<sub>n</sub></em>(<em>a,b</em>))/<em>P</em>(<em>a,b</em>) ≤ (1 −<em>q<sup>2</sup>)</em><sup>n+1</sup>/(2<em>n</em>+1)<sup>2</sup></p> <p>≤ (1/(2<em>n</em>+1)<sup>2</sup>) <em>e<sup>-q^</sup></em><sup>2(<em>n</em>+1)</sup>,&nbsp;&nbsp;</p> <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>true for <em>n</em> ∈ N and <em>q </em>= <em>b</em>/<em>a</em> ∈ [0,1].</p> </div> </div> </div> </div> </div> </div> Vito Lampret Copyright (c) 2019 CUBO, A Mathematical Journal 2019-08-10 2019-08-10 21 2 51 64 10.4067/S0719-06462019000200051 Generalized trace pseudo-spectrum of matrix pencils http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2159 <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>The objective of the study was to investigate a new notion of generalized trace pseudo- spectrum for an matrix pencils. In particular, we prove many new interesting properties of the generalized trace pseudo-spectrum. In addition, we show an analogue of the spectral mapping theorem for the generalized trace pseudo-spectrum in the matrix algebra.</p> </div> </div> </div> Aymen Ammar Aref Jeribi Kamel Mahfoudhi Copyright (c) 2019 CUBO, A Mathematical Journal 2019-08-10 2019-08-10 21 2 65–76 65–76 10.4067/S0719-06462019000200065 Certain results for η-Ricci Solitons and Yamabe Solitons on quasi-Sasakian 3-Manifolds http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2160 <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>We classify quasi-Sasakian 3-manifold with proper η-Ricci soliton and investigate its geometrical properties. Certain results of Yamabe soliton on such manifold are also presented. Finally, we construct an example of non-existence of proper η-Ricci soliton on 3-dimensional quasi-Sasakian manifold to illustrate the results obtained in previous section of the paper.</p> </div> </div> </div> Sunil Kumar Yadav Abhishek Kushwaha Dhruwa Narain Copyright (c) 2019 CUBO, A Mathematical Journal 2019-08-10 2019-08-10 21 2 77–98 77–98 10.4067/S0719-06462019000200077