Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> vol. 34 num. 4 lang. en <![CDATA[SciELO Logo]]> <![CDATA[<strong>The multi-step homotopy analysis method for solving fractional-order model for HIV infection of CD4+T cells</strong>]]> HIV infection of CD4+T cells is one of the causes of health problems and continues to be one of the significant health challenges. This paper presents approximate analytical solutions to the model of HIV infection of CD4+T cells of fractional order using the multi-step ho-motopy analysis method (MHAM). The proposed scheme is only a simple modification of the homotopy analysis method (HAM), in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding problems. The fractional derivatives are described in the Caputo sense. A comparative study between the new algorithm and the classical Runge-Kutta method is presented in the case of integer-order derivatives. The solutions obtained are also presented graphically. <![CDATA[<strong>Inequalities of Hermite-Hadamard Type for h-Convex Functions on Linear Spaces</strong>]]> Some inequalities of Hermite-Hadamard type for h-convex functions defined on convex subsets in real or complex linear spaces are given. Applications for norm inequalities are provided as well. <![CDATA[<strong>Comment on "Edge Geodetic Covers in Graphs</strong>]]> In this paper we show by counter example that one of the main results in the paper "Edge Geodetic Covers in Graphsby Mariano and Canoy (International Mathematical Forum, 4, 2009, no. 46, 2301 - 2310) does not hold. Further, we partially characterize connected graphs G of order n for which its edge geodetic number g e(G) = n - 1. <![CDATA[<strong>Hypo-k-Totally Magic Cordial Labeling of Graphs</strong>]]> A graph G is said to be hypo-k-totally magic cordial if G - {v} is k-totally magic cordial for each vertex v in V(G). In this paper, we establish that cycle, complete graph, complete bipartite graph and wheel graph admit hypo-k-totally magic cordial labeling and some families of graphs do not admit hypo-k-totally magic cordial labeling. <![CDATA[<strong>On the hyperstability of a Cauchy-Jensen type functional equation in Banach spaces</strong>]]> In this paper, we establish some hyperstability results of the following Cauchy-Jensen functional equation <img src="http:/fbpe/img/proy/v34n4//art05_fig1.jpg" width="400" height="40"> in Banach spaces. <![CDATA[<strong>Computing the maximal signless Laplacian index among graphs of prescribed order and diameter</strong>]]> A bug Bug p,r1r2 is a graph obtained from a complete graph Kp by deleting an edge uv and attaching the paths Pri and Pr2 by one of their end vertices at u and v, respectively. Let Q(G) be the signless Laplacian matrix of a graph G and q1(G) be the spectral radius of Q(G). It is known that the bug<img src="http:/fbpe/img/proy/v34n4//art06_fig1.jpg" width="300" height="59"> maximizes q1(G) among all graphs G of order n and diameter d. For a bug B of order n and diameter d, n - d is an eigenvalue of Q(B) with multiplicity n - d - 1. In this paper, we prove that remainder d +1 eigenvalues of Q(B), among them q1(B), can be computed as the eigenvalues of a symmetric tridiagonal matrix of order d +1. Finally, we show that q1(B0) can be computed as the largest eigenvalue of a symmetric tridiagonal matrix of order<img src="http:/fbpe/img/proy/v34n4//art06_fig2.jpg" width="80" height="56"> whenever d is even. <![CDATA[<strong>The Banach-Steinhaus Theorem in Abstract Duality Pairs</strong>]]> Let E, F be sets and G a Hausdorff, abelian topological group with b : E X F→ G; we refer to E, F, G as an abstract duality pair with respect to G or an abstract triple and denote this by (E,F : G). Let (Ei,Fi : G) be abstract triples for i = 1, 2. Let Fi be a family of subsets of Fi and let τFi(Ei) = τi be the topology on Ei of uniform convergence on the members of Fi. Let J be a family of mappings from Ei to E2. We consider conditions which guarantee that J is τ1-τ2equicontinuous. We then apply the results to obtain versions of the Banach-Steinhaus Theorem for both abstract triples and for linear operators between locally convex spaces. <![CDATA[<strong>A New Closed Graph Theorem on Product Spaces</strong>]]> We obtain a new version of closed graph theorem on product spaces. Fernandez’s closed graph theorem for bilinear and multilinear mappings follows as a special case.