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vol. 37 num. 1 lang. pt<![CDATA[SciELO Logo]]>https://scielo.conicyt.cl/img/en/fbpelogp.gif
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<![CDATA[The fixed point and the common fixed point properties in finite pseudo-ordered sets]]>
https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100001&lng=pt&nrm=iso&tlng=pt
Abstract: In this paper, we first prove that every finite nonempty pseudo-ordered with a least element has the least fixed point property and the least common fixed point property for every finite commutative family of self monotone maps. Dually, we establish that a finite nonempty pseudo-ordered with a greatest element has the greatest fixed point property and the greatest common fixed point property for every finite commutative family of self monotone maps. Secondly, we prove that every monotone map ƒ defined on a nonempty finite pseudo-ordered (X, ⊵) has at least a fixed point if and only if there is at least an element ɑ of X such that the subset of X defined by {ƒn(ɑ) : n ∈ ℕ } has a least or a greatest element. Furthermore, we show that the set of all common fixed points of every finite commutative family of monotone maps defined on a finite nonempty complete trellis is also a nonempty complete trellis.<![CDATA[Vertex graceful labeling of some classes of graphs]]>
https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100019&lng=pt&nrm=iso&tlng=pt
Abstract: A connected graph G = (V,E) of order atleast two, with order p and size q is called vertex-graceful if there exists a bijection ʄ : V → { 1, 2, 3, ··· p } such that the induced function ʄ*: E → { 0, 1, 2, ··· q-1} defined by ʄ*(uv) = (ʄ(u)+ ʄ(v)) (mod q) is a bijection. The bijection ʄ is called a vertex-graceful labeling of G. A subset S of the set of natural numbers N is called consecutive if S consists of consecutive integers. For any set X, a mapping ʄ : X → N $ is said to be consecutive if ʄ(X) is consecutive. A vertex-graceful labeling ʄ is said to be strong if the function ʄ1: E → N defined by ʄ1(e)= ʄ(u) + ʄ(v) for all edges e = uv in E forms a consecutive set. It is proved that one vertex union of odd number of copies of isomorphic caterpillars is vertex-graceful and any caterpillar is strong vertex-graceful. It is proved that a spider with even number of legs (paths) of equal length appended to each vertex of an odd cycle is vertex-graceful. It is also proved that the graph lA(mj,n) is vertex-graceful for both n and l odd, 0 ≤ i ≤ n-1, 1 ≤ j ≤ mi. Further, it is proved that the graph A(mj, n) is strong vertex-graceful for n odd, 0 ≤ i ≤ n-1, 1 ≤ j ≤ mi.<![CDATA[A variant of the quadratic functional equation on semigroups]]>
https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100045&lng=pt&nrm=iso&tlng=pt
Abstract: Let S be a semigroup, let H be an abelian group which is uniquely 2-divisible, and let σ be an involutive automorphism of S. We express the solutions : S → H of the following variant of the quadratic functional equation (xy)+𝑓(σ(y)x)=2𝑓(x)+2𝑓(y), x,y ∈ S, in terms of bi-additive maps and solutions of the symmetrized additive Cauchy equation.<![CDATA[A double inequality related with Burnside's formula]]>
https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100057&lng=pt&nrm=iso&tlng=pt
Abstract: We prove the following double inequality related with Burnside's formula for n! where the constants a*=0.428844044... and a*=0.5 are the best possible. We believe that the method we used in the proof gives insight to undergraduate students to understand how simple inequalities can be established.<![CDATA[Intuitionistic fuzzy <em>n</em> -normed algebra and continuous product]]>
https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100068&lng=pt&nrm=iso&tlng=pt
Abstract: In this paper we extend the notion of intuitionistic fuzzy 𝘯-normed linear space (IFnNLS) to define an intuitionistic fuzzy n-normed algebra (IFnNA). We give a necessary and sufficient condition for an IFnNA to be with continuous product. Further, the concept of multiplicatively continuous product has been introduced and related results have been established. Illustrative examples have been provided in support of our results.<![CDATA[Fine spectrum of the upper triangular matrix U(𝒓,0,0,𝒔) over the sequence spaces 𝒄₀ and 𝒄]]>
https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100085&lng=pt&nrm=iso&tlng=pt
Abstract: Fine spectra of various matrices have been examined by several authors. In this article we have determined the fine spectrum of the upper triangular matrix U(r,0,0,s) on thesequence spaces c₀ and c.<![CDATA[Cosine families of operators in a class of Fréchet spaces]]>
https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100103&lng=pt&nrm=iso&tlng=pt
Abstract: M. sova ((10)) proved that the infinitesimal generator of all uniformly continuous cosine family, of operators in Banach space, is a bounded operator. We show by counter-example that the result mentioned above is not true in general on Fréchet spaces, and we prove that the infinitesimal generator of an uniformly continuous cosine family of operators in a class of Fréchet spaces (quojection) is necessarily continuous.<![CDATA[Generalized Drazin-type spectra of Operator matrices]]>
https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100119&lng=pt&nrm=iso&tlng=pt
Abstract: In this paper, we investigate the limit points set of surjective and approximate point spectra of upper triangular operator matrices . We prove that σ*(MC) ∪ W=σ*(𝐴)∪σ*(𝐵) where W is the union of certain holes in σ*(MC), which happen to be subsets of σlgD(𝐵) ∩ σrgD(𝐴), σ* ∈ {σlgD, σrgD} are the limit points set of surjective and approximate point spectra. Furthermore, several sufficient conditions for σ* (MC) = σ* (𝐴)∪σ* (𝐵) holds for every C ∈ ℬ(Y,X) are given.<![CDATA[Some new Ostrowski type fractional integral inequalities for generalized (s,m, φ)-preinvex functions via Caputo <em>k</em> -fractional derivatives]]>
https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100133&lng=pt&nrm=iso&tlng=pt
Abstract: In the present paper, the notion of generalized (s, m, φ)-preinvex function is applied to establish some new generalizations of Ostrowski type integral inequalities via Caputo k-fractional derivatives. At the end, some applications to special means are given.<![CDATA[Sequentially spaces and the finest locally K-convex of topologies having the same onvergent sequences]]>
https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100153&lng=pt&nrm=iso&tlng=pt
Abstract: The present paper is concerned with the concept of sequentially topologies in non-archimedean analysis. We give characterizations of such topologies.<![CDATA[Jordan triple derivation on alternative rings]]>
https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100171&lng=pt&nrm=iso&tlng=pt
Abstract: Let D be a mapping from an alternative ring R into itself satisfying D(a · ba) = D(a) · ba+ a · D(b)a +a · bD(a) for all a, b ∈ R. Under some conditions on R, we show that D is additive.