Proyecciones (Antofagasta, On line) <p align="justify">La revista&nbsp;Proyecciones. Journal of Mathematics es una publicación científica, sin fines de lucro, oficial de la Universidad Católica del Norte, Antofagasta, Chile. Fue fundada en 1982 y depende del Departamento de Matemáticas de la Universidad Católica del Norte.<br>Proyecciones. Journal of Mathematics edita un volumen con 5 números al año.</p> Universidad Católica del Norte. en-US Proyecciones (Antofagasta, On line) 0717-6279 <div id="deed-conditions" class="row"> <ul class="license-properties col-md-offset-2 col-md-8" dir="ltr"> <li class="license by"> <p><strong>Attribution</strong> — You must give <a id="appropriate_credit_popup" class="helpLink" tabindex="0" title="" href="" data-original-title="">appropriate credit</a>, provide a link to the license, and <a id="indicate_changes_popup" class="helpLink" tabindex="0" title="" href="" data-original-title="">indicate if changes were made</a>. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.<span id="by-more-container"></span></p> </li> </ul> </div> <div class="row"> <ul id="deed-conditions-no-icons" class="col-md-offset-2 col-md-8"> <li class="license"><strong>No additional restrictions</strong> — You may not apply legal terms or <a id="technological_measures_popup" class="helpLink" tabindex="0" title="" href="" data-original-title="">technological measures</a> that legally restrict others from doing anything the license permits.</li> </ul> </div> On the hereditary character of certain spectral properties and some applications <p><em>In this paper we study the behavior of certain spectral properties of an operator T on a proper closed and T-invariant subspace W ⊆ X such that T<sup>n </sup>(X) ⊆ W, for some n ≥ 1, where T ∈ L(X) and X is an infinite-dimensional complex Banach space. We prove that for these subspaces a large number of spectral properties are transmitted from T to its restriction on W and vice-versa. As consequence of our results, we give conditions for which semiFredholm spectral properties, as well as Weyl type theorems, are equivalent for two given operators. Additionally, we give conditions under which an operator acting on a subspace can be extended on the entire space preserving the Weyl type theorems. In particular, we give some applications of these results for integral operators acting on certain functions spaces.</em></p> <p> </p> Carlos Rafael Carpintero Ennis Rafael Rosas Rodriguez Orlando J. García Mojica José Eduardo Sanabria Andrés Malaver Copyright (c) 2021 Carlos Rafael Carpintero, Ennis Rafael Rosas Rodriguez, Orlando J. García Mojica, José Eduardo Sanabria, A. Malaver 2021-08-04 2021-08-04 40 5 1053 1069 10.22199/issn.0717-6279-3678 Infinitely many solutions for anisotropic elliptic equations with variable exponent <p><em>In this article, we study the existence and multiplicity of solutions for a class of anisotropic elliptic equations</em></p> <p><em><img src="" alt="" width="483" height="56" /></em></p> <p><em>First we establisch that anisotropic space is separable and by using the Fountain theorem, and dual Fountain theorem we prove, under suitable conditions, that the problem (P) admits two sequences of weak solutions.</em></p> Abdelrachid El Amrouss Ali El Mahraoui Copyright (c) 2021 Abdelrachid El Amrouss, Ali El Mahraoui 2021-09-29 2021-09-29 40 5 1071 1096 10.22199/issn.0717-6279-3921 k-super cube root cube mean labeling of graphs <p><em>Consider a graph G with |V (G)| = p and |E(G)| = q and let f : V (G) → {k, k + 1, k + 2, . . . p + q + k − 1}} be an injective function. The induced edge labeling f ∗ for a vertex labeling f is defined by f ∗ (e) = <img src="" alt="" width="201" height="41" /></em></p> <p><em>for all e = uv ∈ E(G) is bijective. If f(V (G)) ∪ {f ∗ (e) : e ∈ E(G)} = {k, k + 1, k + 2, . . . , p + q + k − 1}, then f is called a k-super cube root cube mean labeling. If such labeling exists, then G is a k-super cube root cube mean graph. In this paper, I introduce k-super cube root cube mean labeling and prove the existence of this labeling to the graphs viz., triangular snake graph T<sub>n</sub>, double triangular snake graph D(T<sub>n</sub>), Quadrilateral snake graph Q<sub>n</sub>, double quadrilateral snake graph D(Q<sub>n</sub>), alternate triangular snake graph A(T<sub>n</sub>), alternate double triangular snake graph AD(Tn), alternate quadrilateral snake graph A(Q<sub>n</sub>), &amp; alternate double quadrilateral snake graph AD(Q<sub>n</sub>).</em></p> V. Princy Kala Copyright (c) 2021 V. Princy Kala 2021-09-29 2021-09-29 40 5 1097 1116 10.22199/issn.0717-6279-4258 Existence of solutions of boundary value problems for nonlinear fractional differential equations with integral conditions <p><em>In this work we investigate the existence and uniqueness of solutions of boundary value problems for fractional differential equations involving the Caputo fractional derivative with integral conditions and the nonlinear term depends on the fractional derivative of an unknown function. Our existence results are based on Banach contraction principle and Schauder fixed point theorem. Two examples are provided to illustrate our results.</em></p> Ahcene Boukehila Copyright (c) 2021 Ahcene Boukehila 2021-09-29 2021-09-29 40 5 1117 1135 10.22199/issn.0717-6279-4271 Sequence spaces defined via Euler method and matrix transformations <p><em>A blend of matrix summability and Euler summability transformation methods is used to define Lacunary sequence spaces defined over n-normed space. Then we present the properties of this space and finally, some inclusion relations are presented. </em></p> Pranav Sharma Copyright (c) 2021 Pranav Sharma 2021-09-29 2021-09-29 40 5 1137 1145 10.22199/issn.0717-6279-5119 Vertex cover and Edge vertex domination in trees <p><em>Let G = (V,E) be a simple graph. An edge e ∈ E(G) edge-vertex dominates a vertex v ∈ V (G) if e is incident with v or e is incident with a vertex adjacent to v. A subset D ⊆ E(G) is an edge-vertex dominating set of a graph G if every vertex of G is edge-vertex dominated by an edge of D. A vertex cover of G is a set C ⊆ V such that for each edge uv ∈ E at least one of u and v is in C. We characterize trees with edge-vertex domination number equals vertex covering number.</em></p> B. Senthilkumar H. Naresh Kumar Y. B. Venkatakrishnan Copyright (c) 2021 B. Senthilkumar, H. Naresh Kumar, Y. B. Venkatakrishnan 2021-09-29 2021-09-29 40 5 1147 1154 10.22199/issn.0717-6279-3532 Some hyperstability results of a p-radical functional equation related to quartic mappings in non-archimedean Banach spaces <p><em>The aim of this paper is to introduce and solve the following p-radical functional equation related to quartic mappings </em></p> <p><em><img src="" alt="" width="677" height="44" /></em></p> <p><em>where f is a mapping from R into a vector space X and p ≥ 3 is an odd natural number. Using an analogue version of Brzd¸ek’s fixed point theorem [13], we establish some hyperstability results for the considered equation in non-Archimedean Banach spaces. Also, we give some hyperstability results for the inhomogeneous p-radical functional equation related to quartic mapping.</em></p> <p><em><img src="" alt="" width="677" height="44" /></em></p> Ahmed Nuino Mustapha Esseghyr Hryrou Samir Kabbaj Copyright (c) 2021 Ahmed Nuino, Mustapha Esseghyr Hryrou, Samir Kabbaj 2021-06-16 2021-06-16 40 5 1155 1177 10.22199/issn.0717-6279-3704 Solution of linear and non-linear partial differential equation of fractional order <p><em>We know that the solution of partial differential equations by analytical method is better than the solution by approximate or series solution method. In this paper, we discuss the solution of linear and non-linear fractional partial differential equations involving derivatives with respect to time or space variables by converting them into the partial differential equations of integer order. Also we develop an analytical formulation to solve such fractional partial differential equations. Moreover, we discuss the method to solve the fractional partial differential equations in space as well as time variables simultaneously with the help of some examples.</em></p> Raju Muneshwar K. L. Bondar Y. H. Shirole Copyright (c) 2021 Raju Muneshwar, K. L. Bondar, Y. H. Shirole 2021-06-16 2021-06-16 40 5 1179 1195 10.22199/issn.0717-6279-4396 A new generalized refinements of Young’s inequality <p><em>In this paper, we show a new generalized refinement of Young's inequality. As applications we give some new generalized refinements of Young type inequalities for the traces, determinants, and norms of positive definite matrices.</em></p> <p> </p> Mohamed Amine Ighachane Mohamed Akkouchi Copyright (c) 2021 Mohamed Amine Ighachane, Mohamed Akkouchi 2021-04-19 2021-04-19 40 5 1197 1209 10.22199/issn.0717-6279-4468 Extended study of biological networks using graph theory <p><em>We represent biological networks by a function that maps the structure of a network to a number called topological index. Topological indices have been studied for biological networks in which a person transmits a virus to two other people, and a person having the virus is in contact with exactly one other person who got the virus from someone else. We extend research in this area by studying biological networks in which a person transmits a virus to n other people, where n ≥ 2, and a person having the virus is in contact with p other people (0 ≤ p ≤ n-2) who got the virus from some other person.</em></p> Tomáš Vetrík Copyright (c) 2021 Tomas Vetrik 2021-04-19 2021-04-19 40 5 1211 1225 10.22199/issn.0717-6279-4580 On ideal convergence of triple sequences in intuitionistic Fuzzy normed space defined by compact operator <p><em>The main purpose of this article is to introduce and study some new spaces of I-convergence of triple sequences in intuitionistic fuzzy normed space defined by compact operator i.e <sub>3</sub>S<sup>I</sup> <sub>(μ,ν)</sub>(T ) and <sub>3</sub>S<sup>I</sup><sub>0(μ,ν)</sub>(T ) and examine some fundamental properties, fuzzy topology and verify inclusion relations lying under these spaces.</em></p> Vakeel A. Khan Mohd. Imran Idrisi Umme Tuba Copyright (c) 2021 Vakeel A. Khan, Mohd. Imran Idrisi, Umme Tuba 2021-09-29 2021-09-29 40 5 1227 1247 10.22199/issn.0717-6279-3614 Separation axioms of αm-contra-open maps and b-ω-open sets in generalized topological spaces <p><em>In this paper, we introduce T<sub>α</sub>m-Super-Spaces, α<sup>m</sup>-contra-closed maps, α<sup>m</sup>-contra-open maps, α<sup>m</sup>-contra-continuous maps, α<sup>m</sup>-contrairresolute maps, b-ω-open sets and Continuity via b-ω-open sets and studied some of their properties</em></p> Boulbaba Ghanmi Rim Messaoud Amira Missaoui Copyright (c) 2021 Boulbaba Ghanmi, Rim Messaoud, Amira Missaoui 2021-09-29 2021-09-29 40 5 1249 1266 10.22199/issn.0717-6279-3935 On the total irregularity strength of convex polytope graphs <p><em>A vertex (edge) irregular total k-labeling ? of a graph G is a labeling of the vertices and edges of G with labels from the set {1,2,...,k} in such a way that any two different vertices (edges) have distinct weights. Here, the weight of a vertex x in G is the sum of the label of x and the labels of all edges incident with the vertex x, whereas the weight of an edge is the sum of label of the edge and the vertices incident to that edge. The minimum k for which the graph G has a vertex (edge) irregular total k-labeling is called the total vertex (edge) irregularity strength of G. In this paper, we are dealing with infinite classes of convex polytopes generated by prism graph and antiprism graph. We have determined the exact value of their total vertex irregularity strength and total edge irregularity strength.</em></p> Syed Ahtshma Ul Haq Bokhary Muhammad Imran Usman Ali Copyright (c) 2021 Syed Ahtshma Ul Haq Bokhary, Muhammad Imran, Usman Ali 2021-06-23 2021-06-23 40 5 1267 1277 10.22199/issn.0717-6279-3959 On a fuzzy metric space and fuzzy convergence <p><em>In this paper we introduce a new type of fuzzy metric space and obtain several properties of it. Also some topological properties and boundedness are investigated. The notion of convergence of fuzzy sequences together with the notion of fuzzy cauchy sequences in a fuzzy metric space are discussed and some basic results related to these notions are investigated.</em></p> Alias B. Khalaf Maha W. Abdulqader Copyright (c) 2021 Alias B. Khalaf, Maha W. Abdulqader 2021-04-28 2021-04-28 40 5 1279 1299 10.22199/issn.0717-6279-3986 The distribution of zeros of solutions for a class of third order differential equation <p><em>For third order linear differential equations of the form</em></p> <p>r(t)x'(t)''+ p(t)x'(t) + q(t)x(t) = 0;<br /><em>we will establish lower bounds for the distance between zeros of a solution and/or its derivatives. The main results will be proved by making use of Hardyís inequality, some generalizations of Opialís inequality and Boydís inequality.</em><br /><br /></p> Clemente Cesarano Mohammed A. Arahet Tareq M. Al-Shami Copyright (c) 2021 Clemente Cesarano, Mohammed A. Arahet, Tareq M. Al-Shami 2021-09-29 2021-09-29 40 5 1301 1321 10.22199/issn.0717-6279-4002 On degree of approximation of Fourier series of functions in Besov space using Nörlund mean <p><em>In the present article, we have established a result on degree of approximation of function in the Besov space by (N; r<sub>n</sub>)- mean of Trigonometric Fourier series</em></p> Birupakhya Prasad Padhy Anwesha Mishra U. K. Misra Copyright (c) 2021 Birupakhya Prasad Padhy, Anwesha Mishra, U. K. Misra 2021-04-19 2021-04-19 40 5 1323 1340 10.22199/issn.0717-6279-4092 Unit groups of group algebras of Abelian groups of order 32 <p><em>Let F be a finite field of characteristic p &gt; 0 with q = p<sup>n</sup> elements. In this paper, a complete characterization of the unit groups U(F G) of group algebras F G for the abelian groups of order 32, over finite field of characteristic p &gt; 0 has been obtained.</em></p> Suchi Bhatt Harish Chandra Copyright (c) 2021 Suchi Bhatt, Harish Chandra 2021-09-29 2021-09-29 40 5 1341 1356 10.22199/issn.0717-6279-4374