https://www.revistaproyecciones.cl/issue/feed Proyecciones (Antofagasta, On line) 2020-02-12T15:55:31+00:00 Ricardo Soto Montero rsoto@ucn.cl Open Journal Systems https://www.revistaproyecciones.cl/article/view/3250 Strongly convexity on fractal sets and some inequalities 2020-02-05T00:08:38+00:00 Rainier V. Sánchez C. rainiersan76@gmail.com José Eduardo Sanabria jesanabri@gmail.com <p>We introduce a generalization of the concept of a strongly convex function on a fractal set, study some algebraic properties and establish Jensen-type and Hermite-Hadamard-type inequalities.</p> 2020-02-04T00:00:00+00:00 Copyright (c) 2020 Rainier V. Sánchez C., José Eduardo Sanabria https://www.revistaproyecciones.cl/article/view/3968 Nondifferentiable higher-order duality theorems for new type of dual model under generalized functions 2020-02-05T00:08:38+00:00 Ramu Dubey rdubeyjiya@gmail.com Vishnu Narayan Mishra vishnunarayanmishra@gmail.com <p><em>The motivation behind this article is to study a class of nondifferentiable multiobjective fractional programming problem in which each component of objective functions contains a term including the support function of a compact convex set. For a differentiable function, we consider a class of higher order pseudo quasi/ strictly pseudo quasi/weak strictly pseudo quasi- (V, </em><em>ρ</em><em>, d)-type-I convex functions. Under these the higher-order pseudo quasi/ strictly pseudo quasi/weak strictly pseudo quasi- (V, </em><em>ρ</em><em>, d)-type-I convexity assumptions, we prove the higher-order weak, higher-order strong and higher-order converse duality theorems related to efficient solution.</em></p> 2020-02-04T00:00:00+00:00 Copyright (c) 2020 Ramu Dubey, Vishnu Narayan Mishra https://www.revistaproyecciones.cl/article/view/3969 Zk-magic labeling of star of graphs 2020-02-05T00:08:39+00:00 P. Jeyanthi jeyajeyanthi@rediffmail.com K. Jeya Daisy jeyadaisy@yahoo.com <p><em>For any non-trivial abelian group A under addition a graph G is said to be A-magic if there exists a labeling f : E(G) → A − {0} such that, the vertex labeling f <sup>+</sup> defined as f <sup>+</sup>(v) = Pf(uv) taken over all edges uv incident at v is a constant. An A-magic graph G is said to be Z<sub>k</sub>-magic graph if the group A is Z<sub>k</sub>, the group of integers modulo k and these graphs are referred to as k-magic graphs. In this paper we prove that the graphs such as star of cycle, flower, double wheel, shell, cylinder, gear, generalised Jahangir, lotus inside a circle, wheel, closed helm graph are Z<sub>k</sub>-magic graphs.</em></p> 2020-02-04T00:00:00+00:00 Copyright (c) 2020 P. Jeyanthi, K. Jeya Daisy https://www.revistaproyecciones.cl/article/view/3975 Partition of the spectra for the lower triangular double band matrix as generalized difference operator Δv over the sequence spaces c and lp (1 < p < ∞) 2020-02-05T00:08:39+00:00 Nuh Durna ndurna@cumhuriyet.edu.tr <p><em>Let the sequence (v<sub>k</sub>) is assumed to be either constant or strictly decreasing sequence of positive real numbers satisfying lim<sub>k→∞</sub> v<sub>k</sub> = L &gt; 0 and sup<sub>k</sub> v<sub>k</sub> ≤ 2L. Then the generalized difference operator Δ<sub>v</sub> is Δ<sub>v</sub> x = Δ<sub>v</sub> (x<sub>n</sub>) = (v<sub>n</sub>x<sub>n</sub> − v<sub>n−1</sub>x<sub>n−1</sub>)<sup>∞</sup> <sub>n=0</sub> with x<sub>−1</sub> = v<sub>−1</sub> = 0. The aim of this paper is to obtain the approximate point spectrum, the defect spectrum and the compression spectrum of the operator Δ<sub>v</sub> and modified of the operator Δ<sub>v</sub> on the sequence spaces c and </em><em>????</em><em><sub>p</sub></em><em> (1 &lt; p &lt; ∞).</em></p> 2020-02-04T00:00:00+00:00 Copyright (c) 2020 Nuh Durna https://www.revistaproyecciones.cl/article/view/3980 Some hyperstability results for a Cauchy-Jensen type functional equation in 2-Banach spaces 2020-02-05T00:08:39+00:00 Khaled Yahya Naif Sayar khaledsayar@gmail.com Amal Bergam bergamamal11@gmail.com <p>In this paper, we investigate some stability and hyperstability results for the following Cauchy-Jensen functional equation</p> <p>in 2-Banach spaces by using Brzdȩk’s fixed point approach.</p> <p>&nbsp;</p> 2020-02-04T00:00:00+00:00 Copyright (c) 2020 Khaled Yahya Naif Sayar, Amal Bergam https://www.revistaproyecciones.cl/article/view/2938 Some ideal convergent multiplier sequence spaces using de la Vallee Poussin mean and Zweier operator 2020-02-05T00:08:39+00:00 Tanweer Jalal tjalal@nitsri.net <p>We introduce multiplier type ideal convergent sequence spaces, using Zweier transform and de la Vallee Poussin mean. We study some topological and algebraic properties of these spaces. Further we prove some inclusion relations related to these spaces.</p> 2020-02-04T00:00:00+00:00 Copyright (c) 2020 Tanweer Jalal https://www.revistaproyecciones.cl/article/view/3981 General solution and hyperstability results for a cubic radical functional equation related to quadratic mapping 2020-02-05T00:08:40+00:00 Rachid El Ghali rachid2810@gmail.com Muaadh Almahalebi muaadh1979@hotmail.fr Samir Kabbaj samkabbaj@yahoo.fr <p>The aim of this paper is to introduce and solve the following radical cubic functional equation</p> <p><img src="/public/site/images/rvidal/formula20.png"></p> <p>Also, we investigate some stability results for the considered equation in Banach spaces.</p> 2020-02-04T00:00:00+00:00 Copyright (c) 2020 Rachid El Ghali, Muaadh Almahalebi, Samir Kabbaj https://www.revistaproyecciones.cl/article/view/3875 Weak convergence and weak compactness in the space of integrable functions with respect to a vector meansure 2020-02-05T00:08:40+00:00 Charles Swartz cswartz@nmsu.edu <p>We consider weak convergence and weak compactness in the space <em>L<sup>1</sup>(m)</em> of real valued integrable functions with respect to a Banach space calued measure <em>m&nbsp;</em>equipped with its natural norm. We give necessary and sufficient conditions for a sequence in <em>L<sup>1</sup>(m)&nbsp;</em>to be weak Cauchy, and we give necessary and sufficient conditions for a subset of <em>L<sup>1</sup>(m)&nbsp;</em>to be conditionally sequentially weakly compact.</p> 2020-02-04T00:00:00+00:00 Copyright (c) 2020 Charles Swartz https://www.revistaproyecciones.cl/article/view/3305 A cryptography method based on hyperbolic balancing and Lucas-balancing functions 2020-02-05T00:08:40+00:00 Prasanta Kumar Ray prasantamath@suniv.ac.in <p><em>The goal is to study a new class of hyperbolic functions that unite the characteristics of the classical hyperbolic functions and the recurring balancing and Lucas-balancing numbers. These functions are indeed the extension of Binet formulas for both balancing and Lucas-balancing numbers in continuous domain. Some identities concerning hyperbolic balancing and Lucas-balancing functions are also established. Further, a new class of square matrices, a generalization of balancing Q<sub>B</sub>-matrices for continuous domain, is considered. These matrices indeed enable us to develop a cryptography method for secrecy purpose.</em></p> 2020-02-04T00:00:00+00:00 Copyright (c) 2020 Prasanta Kumar Ray https://www.revistaproyecciones.cl/article/view/3983 Some refinements to Hölder’s inequality and applications 2020-02-05T00:08:41+00:00 Mohamed Akkouchi akkm555@yahoo.fr Mohamed Amine Ighachane mohamedamineighachane@gmail.com <p><em>We establish some new refinements to the Hölder inequality. We then apply them to provide some refinements to the extended Euler’s gamma and beta functions. As another application of our results, we give a new proof of the equivalence between the Hölder inequality and the Cauchy-Schwarz inequality.</em></p> 2020-02-04T00:00:00+00:00 Copyright (c) 2020 Mohamed Akkouchi, Mohamed Amine Ighachane https://www.revistaproyecciones.cl/article/view/3984 The total double geodetic number of a graph 2020-02-05T00:08:41+00:00 A. P. Santhakumaran apskumar1953@gmail.com T. Jebaraj jebaraj.math@gmail.com <p><em>For a connected graph G of order n, a set S of vertices is called a double geodetic set of G if for each pair of vertices x, y in G there exist vertices u, v </em><em>∈</em><em> S such that x, y </em><em>∈</em><em> I[u, v]. The double geodetic number dg(G) is the minimum cardinality of a double geodetic set. Any double godetic set of cardinality dg(G) is called a dg-set of G. A connected double geodetic set of G is a double geodetic set S such that the subgraph G[S] induced by S is connected. The mínimum cardinality of a connected double geodetic set of G is the connected double geodetic number of G and is denoted by dgc(G). A connected double geodetic set of cardinality dgc(G) is called a dgc-set of G. A total double geodetic set of a graph G is a double geodetic set S such that the subgraph G[S] induced by S has no isolated vertices. The minimum cardinality of a total double geodetic set of G is the total double geodetic number of G and is denoted by dgt(G). For positive integers r, d and k ≥ 4 with r ≤ d ≤ 2r, there exists a connected graph G with rad G = r, diam G = d and dgt(G) = k. It is shown that if n, a, b are positive integers such that 4 ≤ a ≤ b ≤ n, then there exists a connected graph G of order n with dgt(G) = a and dgc(G) = b. Also, for integers a, b with 4 ≤ a ≤ b and b ≤ 2a, there exists a connected graph G such that dg(G) = a and dgt(G) = b.</em></p> 2020-02-04T00:00:00+00:00 Copyright (c) 2020 A. P. Santhakumaran, T. Jebaraj https://www.revistaproyecciones.cl/article/view/3987 Lie symmetry analysis and traveling wave solutions of equal width wave equation 2020-02-12T15:55:31+00:00 Antim Chauhan antimchauhan1@gmail.com Rajan Arora rajanfpt@iitr.ernet.in Amit Tomar amitmath14@gmail.com <p><em>We obtained the power series solution and the traveling wave solutions of equal width wave equation by using the Lie symmetry method. The fundamental idea behind the symmetry transformation method is that it reduces one independent variables in a system of PDEs by utilizing Lie symmetries and surface invariance condition. We first obtained the infinitesimals and commutation table with the help of MAPLE software. Lie symmetry transformation method (STM) has been applied on EWW equation and converted it into various nonlinear ODEs. Then, the tanh method and the power series method have been applied for solving the reduced nonlinear ordinary differential equations (ODEs). Convergence of the power series solutions has also been shown.</em></p> 2020-02-04T00:00:00+00:00 Copyright (c) 2020 Antim Chauhan, Rajan Arora, Amit Tomar https://www.revistaproyecciones.cl/article/view/3403 A new approach for solving linear fractional integro-differential equations and multi variable order fractional differential equations 2020-02-05T00:08:41+00:00 Fateme Ghomanjani fatemeghomanjani@gmail.com <p><em>In the sequel, the numerical solution of linear fractional integrodifferential equations (LFIDEs) and multi variable order fractional differential equations (MVOFDEs) are found by Bezier curve method (BCM) and operational matrix. Some numerical examples are stated and utilized to evaluate the good and accurate results.</em></p> 2020-02-04T00:00:00+00:00 Copyright (c) 2020 fateme ghomanjani https://www.revistaproyecciones.cl/article/view/3988 Hermite-Hadamard type fractional integral inequalities for products of two MT(r;g,m,φ)-preinvex functions 2020-02-05T00:08:42+00:00 Artion Kashuri artionkashuri@gmail.com Rozana Liko rozanaliko86@gmail.com <p><em>A new class of MT<sub>(r;g,m,φ)-</sub>preinvex functions is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving products of two MT<sub>(r;g,m,φ)-</sub>preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for products of two MT<sub>(r;g,m,φ)-</sub>preinvex functions via Riemann-Liouville fractional integrals are established. These general inequalities give us some new estimates for the left-hand side of Gauss-Jacobi type quadrature formula and Hermite-Hadamard type fractional integral inequalities. At the end, some conclusions and future research are given.</em></p> 2020-02-04T03:06:58+00:00 Copyright (c) 2020 Artion Kashuri, Rozana Liko https://www.revistaproyecciones.cl/article/view/3450 Further common local spectral properties for bounded linear operators 2020-02-05T00:08:42+00:00 Hassane Zguitti hassane.zguitti@usmba.ac.ma <p><em>We study common local spectral properties for bounded linear operators A </em><em>∈ </em><em>ℒ(X,Y)&nbsp;</em><em>and B,C </em><em>∈ </em><em>ℒ (Y,X) such that </em></p> <p><em>A(BA)<sup>2</sup>=ABACA=ACABA=(AC)<sup>2</sup>A.</em></p> <p><em>We prove that AC and BA share the single valued extension property, the Bishop property (β), the property (β<sub>ε</sub>), the decomposition property (δ) and decomposability. Closedness of analytic core and quasinilpotent part are also investigated. Some applications to Fredholm operators are given.</em></p> 2020-02-04T22:31:58+00:00 Copyright (c) 2020 Hassane Zguitti