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 DOAJ, zbMATH Open, MathSciNet, Latindex, Miar, Redib, SciELO-Chile and Scopus.</p> Universidad de La Frontera. Temuco, Chile. en-US CUBO, A Mathematical Journal 0716-7776 The Zamkovoy canonical paracontact connection on a para-Kenmotsu manifold http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2710 <div class="page" title="Page 1"> <div class="section"> <div class="layoutArea"> <div class="column"> <p>The object of the paper is to study a type of canonical linear connection, called the Zamkovoy canonical paracontact connection on a para-Kenmotsu manifold.</p> </div> </div> </div> </div> D. G. Prakasha H. Harish P. Veeresha Venkatesha Copyright (c) 2021 D. G. Prakasha et al. https://creativecommons.org/licenses/by-nc/4.0/ 2021-08-01 2021-08-01 23 2 191–206 191–206 10.4067/S0719-06462021000200191 Coincidence point results of nonlinear contractive mappings in partially ordered metric spaces http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2711 <div class="page" title="Page 1"> <div class="section"> <div class="layoutArea"> <div class="column"> <p>In this paper, we proved some coincidence point results for \(f\)- nondecreasing self-mapping satisfying certain rational type contractions in the context of a metric space endowed with a partial order. Moreover, some consequences of the main result are given by involving integral type contractions in the space. Some numerical examples are illustrated to support our results. As an application, we have discussed the existence of a unique solution of integral equation.</p> </div> </div> </div> </div> K. Kalyani N. Seshagiri Rao Copyright (c) 2021 K. Kalyani et al. https://creativecommons.org/licenses/by-nc/4.0/ 2021-08-01 2021-08-01 23 2 207–224 207–224 10.4067/S0719-06462021000200207 Existence results for a multipoint boundary value problem of nonlinear sequential Hadamard fractional differential equations http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2712 <div class="page" title="Page 1"> <div class="section"> <div class="layoutArea"> <div class="column"> <p>In this paper, existence and uniqueness results are established for a nonlinear sequential Hadamard fractional differential equation with multi-point boundary conditions, via Banach and Krasnosel'skiǐ's<span class="Apple-converted-space">&nbsp;</span>fixed point theorems and Leray-Schauder nonlinear alternative. An example illustrating the existence of a unique solution is also constructed.</p> </div> </div> </div> </div> Bashir Ahmad Amjad F. Albideewi Sotiris K. Ntouyas Ahmed Alsaedi Copyright (c) 2021 B. Ahmad et al. https://creativecommons.org/licenses/by-nc/4.0/ 2021-08-01 2021-08-01 23 2 225–237 225–237 10.4067/S0719-06462021000200225 Free dihedral actions on abelian varieties http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2714 <p class="p1">We give a simple construction for hyperelliptic varieties, defined as the quotient of a complex torus by the action of a finite group \(G\) that contains no translations and acts freely, with \(G\) any dihedral group. This generalizes a construction given by Catanese and Demleitner for \(D_4\) in dimension three.</p> Bruno Aguiló Vidal Copyright (c) 2021 B. Aguiló Vidal https://creativecommons.org/licenses/by-nc/4.0/ 2021-08-01 2021-08-01 23 2 239–244 239–244 10.4067/S0719-06462021000200239 Approximate solution of Abel integral equation in Daubechies wavelet basis http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2715 <div class="page" title="Page 1"> <div class="section"> <div class="layoutArea"> <div class="column"> <p>This paper presents a new computational method for solving Abel integral equation (both first kind and second kind). The numerical scheme is based on approximations in Daubechies wavelet basis. The properties of Daubechies scale functions are employed to reduce an integral equation to the solution of a system of algebraic equations. The error analysis associated with the method is given. The method is illustrated with some examples and the present method works nicely for low resolution.</p> </div> </div> </div> </div> Jyotirmoy Mouley M. M. Panja B. N. Mandal Copyright (c) 2021 J. Mouley et al. https://creativecommons.org/licenses/by-nc/4.0/ 2021-08-01 2021-08-01 23 2 245–264 245–264 10.4067/S0719-06462021000200245 On Rellich’s Lemma, the Poincaré inequality, and Friedrichs extension of an operator on complex spaces http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2716 <div class="page" title="Page 1"> <div class="section"> <div class="layoutArea"> <div class="column"> <p>This paper is mainly concerned with: (i) a generalization of the Rellich’s Lemma to a Riemann subdomain of a complex space, (ii) the Poincaré inequality, and (iii) Friedrichs extension of a Schrödinger type operator. Applications to the eigenfunction expansion problem associated to the modified Laplacian are also given.</p> </div> </div> </div> </div> Chia-chi Tung Pier Domenico Lamberti Copyright (c) 2021 C. Tung et al. https://creativecommons.org/licenses/by-nc/4.0/ 2021-08-01 2021-08-01 23 2 265–285 265–285 10.4067/S0719-06462021000200265 Weakly strongly star-Menger spaces http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2717 <p class="p1">A space \(X\) is called weakly strongly star-Menger space if for each sequence (\(\mathcal{U}_{n} : n \in \omega\)) of open covers of \(X\), there is a sequence \((F_n : n\in\omega)\) of finite subsets of \(X\) such that \(\overline{\bigcup_{n\in\omega} St(F_n, \mathcal{U}_n)}\) is \(X\).<span class="Apple-converted-space">&nbsp;</span>In this paper, we investigate the relationship of weakly strongly star-Menger spaces with other related spaces. It is shown that a Hausdorff paracompact weakly star Menger \(P\)-space is star-Menger. We also study the images and preimages<span class="Apple-converted-space">&nbsp;</span>of weakly strongly star-Menger spaces under various type of maps.</p> Gaurav Kumar Brij K. Tyagi Copyright (c) 2021 G. Kumar et al. https://creativecommons.org/licenses/by-nc/4.0/ 2021-08-01 2021-08-01 23 2 287–298 287–298 10.4067/S0719-06462021000200287 Subclasses of \(\lambda\)-bi-pseudo-starlike functions with respect to symmetric points based on shell-like curves http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2718 <p class="p1">In this paper we define the subclass \(\mathcal{PSL}^\lambda_{s,\Sigma}(\alpha,\tilde{p}(z))\) of the class \(\Sigma\) of bi-univalent functions defined in the unit disk, called \(\lambda\)-bi-pseudo-starlike, with respect to symmetric points, related to shell-like curves connected with Fibonacci numbers. We determine the initial Taylor-Maclaurin coefficients \(|a_2|\) and \(|a_3|\) for functions \(f\in\mathcal{PSL}^\lambda_{s,\Sigma}(\alpha,\tilde{p}(z)).\) Further we determine the Fekete-Szegö result for the function class \(\mathcal{PSL}^\lambda_{s,\Sigma}(\alpha,\tilde{p}(z))\) and for the special cases \(\alpha=0\), \(\alpha=1\) and \(\tau =-0.618\) we state corollaries improving the initial Taylor-Maclaurin coefficients \(|a_2|\) and \(|a_3|\).</p> H. Özlem Güney G. Murugusundaramoorthy K. Vijaya Copyright (c) 2021 H. Özlem Güney et al. https://creativecommons.org/licenses/by-nc/4.0/ 2021-08-01 2021-08-01 23 2 299–312 299–312 10.4067/S0719-06462021000200299 A new class of graceful graphs: \(k\)-enriched fan graphs http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2729 <p class="p1">The Graceful Tree Conjecture stated by Rosa in the mid 1960s says that every tree can be gracefully labelled. It is one of the best known open problems in Graph Theory. The conjecture has caused a great interest in the study of gracefulness of simple graphs and has led to many new contributions to the list of graceful graphs. However, it has to be acknowledged that not much is known about the structure of graceful graphs after 55 years.</p> <p class="p1">Our paper adds an infinite family of classes of graceful graphs to the list of known simple graceful graphs. We introduce classes of \(k\)-enriched fan graphs \(kF_n\) for all integers \(k, n\ge 2\) and we prove that these graphs are graceful. Moreover, we provide characterizations of the \(k\)-enriched fan graphs \(kF_n\) among all simple graphs via Sheppard's labelling sequences introduced in the 1970s, as well as via labelling relations and graph chessboards. These last approaches are new tools for the study of graceful graphs introduced by Haviar and Ivaška in 2015. The labelling relations are closely related to Sheppard's labelling sequences while the&nbsp;graph chessboards provide a nice visualization of graceful labellings. We close our paper with an open problem concerning another infinite family of extended fan graphs.</p> M. Haviar S. Kurtulík Copyright (c) 2021 M. Haviar et al. https://creativecommons.org/licenses/by-nc/4.0/ 2021-08-01 2021-08-01 23 2 313–331 313–331 10.4067/S0719-06462021000200313 On the conformally \(k\)-th Gauduchon condition and the conformally semi-Kähler condition on almost complex manifolds http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2730 <p class="p1">We introduce the \(k\)-th Gauduchon condition on almost complex manifolds. We show that if both the conformally \(k\)-th Gauduchon condition and the conformally semi-Kähler condition are satisfied, then it becomes conformally quasi-Kähler.</p> Masaya Kawamura Copyright (c) 2021 M. Kawamura https://creativecommons.org/licenses/by-nc/4.0/ 2021-08-01 2021-08-01 23 2 333–341 333–341 10.4067/S0719-06462021000200333