Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> vol. 41 num. 3 lang. en <![CDATA[SciELO Logo]]> <![CDATA[Existence of coincidence points for Feng-Liu type multivalued contractions with a singlevalued mapping]]> Abstract In this paper we establish coincidence point results for multivalued Feng-Liu type contractions with a singlevalued mapping. There is a supporting example. Several other existing results are contained in our theorems. <![CDATA[On a subclass of meromorphic functions with positive coefficients defined by rapid operator]]> Abstract In this paper, we introduce and study a new subclass of meromorphic univalent functions defined by Rapid operator. We obtain coefficient inequalities, extreme points, radius of starlikeness and convexity. Finally we obtain partial sums and neighborhood properties for the class ∑* p (γ,κ,μ,θ) <![CDATA[Two-parameter generalization of bihyperbolic Jacobsthal numbers]]> Abstract In this paper, we define a two-parameter generalization of bihyperbolic Jacobsthal numbers. We give Binet formula, the generating functions and some identities for these numbers. <![CDATA[On the resolution of the heat equation in unbounded non-regular domains of R<sup>³</sup>]]> Abstract We will prove well posedness and regularity results for the bidimensional heat equation, subject to mixed Dirichlet-Neumann type boundary conditions on the parabolic boundary of an unbounded (in one space variable direction) time-dependent domain. Our results are proved in anisotropic Hilbertian Sobolev spaces by using the domain decomposition method. This work complements the results obtained in [13] in the one-space variable case. <![CDATA[Lyapunov stability and weak attraction for control systems]]> Abstract In this paper we deal with Lyapunov stability and weak attraction for control systems. We give characterizations of the stability and asymptotical stability of a compact set by means of its components. We also study the asymptotical stability of the prolongation of a compact weak attractor. <![CDATA[Structure of a quotient ring <em>R/P</em> and its relation with generalized derivations of <em>R</em>]]> Abstract The fundamental aim of this paper is to investigate the structure of a quotient ring R/P where R is an arbitrary ring and P is a prime ideal of R. More precisely, we will characterize the commutativity of R/P via the behavior of generalized derivations of R satisfying algebraic identities involving the prime ideal P. Moreover, various wellknown results characterizing the commutativity of prime (semi-prime)rings have been extended. Furthermore, examples are given to prove that the restrictions imposed on the hypothesis of the various theorems were not superfluous. <![CDATA[A new refinement of the generalized Hölder’s inequality with applications]]> Abstract In this paper, we prove a further generalized refinement of the weighted arithmetic-geometric mean inequality. As application, we show a new refinement of the generalized classical Hölder’s inequality and we give refinements to several inequalities for some special functions. <![CDATA[Stability and instability analysis for the standing waves for a generalized Zakharov-Rubenchik system]]> Abstract In this paper, we analyze the stability and instability of standing waves for a generalized Zakharov-Rubenchik system (or the Benney-Roskes system) in spatial dimensions N = 2, 3. We show that the standing waves generated by the set of minimizers for the associated variational problem are stable, for N = 2 and σ(p − 2) &gt; 0. We also show that the standing waves are strongly unstable, for N = 3 and if either σ &lt; 0 and 4/3 &lt;p&lt; 4, or σ &gt; 0 and 0 &lt;p&lt; 2. Results follow by using the variational characterization of standing waves, the concentration compactness principle due to J. Lions and the compactness lemma due to E. Lieb to solve the associated minimization problem. <![CDATA[Spectral operation in locally convex algebras]]> Abstract We show that if A is a spectrally bounded algebra, then all functions operate spectrally on A if and only if SpAx is finite for every x ∈ A. We also prove that if A is a commutative Q-l.m.c.a, then all functions operate spectrally on A if and only if A/RadA is algebraic. Furthermore, if A is a semi-simple commutative Q-l.m.c.a. which is a Baire space, all functions operate spectrally on A if and only if it is isomorphic to C n for some n ∈ N. A structure result concerning semi-simple commutative complete m-convex algebras of countable dimension is also given. <![CDATA[On Δ<sup>ᵐ</sup>-statistical convergence double sequences in intuitionistic fuzzy normed spaces]]> Abstract In the present paper, the basic objective of our work is to define Δᵐ-statistical convergence in the setup of intuitionistic fuzzy normed spaces for double sequences. We have proved some examples which shows this method of convergence is more generalized. Further, we defined the Δᵐ-statistical Cauchy sequences in these spaces and given the Cauchy convergence criterion for this new notion of convergence. <![CDATA[Powers of cycle graph which are <em>k</em>-self complementary and <em>k</em>-co-self complementary]]> Abstract E. Sampath Kumar and L. Pushpalatha [4] introduced a generalized version of complement of a graph with respect to a given partition of its vertex set. Let G = (V,E) be a graph and P = {V₁, V₂,...,Vk} be a partition of V of order k ≥ 1. The k-complement GP k of G with respect to P is defined as follows: For all Vi and Vj in P, i ≠ j, remove the edges between Vi and Vj , and add the edges which are not in G. Analogues to self complementary graphs, a graph G is k-self complementary (k-s.c.) if GP k ≅ G and is k-co-self complementary (k-co.s.c.) if GP k ≅ Ġ with respect to a partition P of V (G). The mth power of an undirected graph G, denoted by Gm is another graph that has the same set of vertices as that of G, but in which two vertices are adjacent when their distance in G is at most m. In this article, we study powers of cycle graphs which are k-self complementary and k-co-self complementary with respect to a partition P of its vertex set and derive some interesting results. Also, we characterize k-self complementary C2 n and the respective partition P of V (C2 n). Finally, we prove that none of the C2 n is k-co-self complementary for any partition P of V (C2 n). <![CDATA[On fuzzy γ<sub>µ</sub>-open sets in generalized fuzzy topological spaces]]> Abstract In this paper, we explore the existence of operation approach on open sets in a generalized fuzzy topological space. We introduce the concept of fuzzy γµ-open set and study some basic properties of it. We obtain an interesting result that the intersection of two fuzzy γµ-open sets may not be a fuzzy γµ-open set, but if the operation is regular then the intersection becomes a fuzzy γµ-open set. We also initiate the notions of fuzzy minimal γµ-open set and fuzzy γµ-locally finite space and establish various results related to these. <![CDATA[Stability problem in a set of Lebesgue measure zero of bi-additive functional equation]]> Abstract Let X be a vector space and Y be a Banach space. Our aim in this paper is to investigate the Hyers-Ulam stability problem of the following bi-additive functional equation f(x + y, s − t) + f(x − y, s + t)=2f(x, s) − 2f(y, t), x, y, s, t ∈ X, where f : X × X → Y . As a consequence, we discuss the stability of the considered functional equation in a restricted domain and in the set of Lebesgue measure zero. <![CDATA[Near-Zumkeller numbers]]> Abstract A positive integer n is called a Zumkeller number if the set of all the positive divisors of n can be partitioned into two disjoint subsets, each summing to σ(n)/2. In this paper, Generalizing further, near-Zumkeller numbers and k-near-Zumkeller numbers are defined and also some results concerning these numbers are established. Relations of these numbers with practical numbers are also studied in this paper. <![CDATA[Convergence of an iteration scheme in convex metric spaces]]> Abstract In this paper, a new iteration scheme in a uniformly convex metric space is defined and its convergence is obtained. A numerical example is also considered to compare the rate of convergences of the iteration with that of an existing iteration scheme.