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vol. 36 num. 1 lang. pt<![CDATA[SciELO Logo]]>http://www.scielo.cl/img/en/fbpelogp.gif
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<![CDATA[<strong>Odd vertex equitable even labeling of graphs</strong>]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000100001&lng=pt&nrm=iso&tlng=pt
In this paper, we introduce a new labeling called odd vertex equitable even labeling. Let G be a graph with p vertices and q edges and A = {1, 3,..., q} if q is odd or A = {1, 3,..., q + 1} if q is even. A graph G is said to admit an odd vertex equitable even labeling if there exists a vertex labeling f : V(G) → A that induces an edge labeling f * defined by f * (uv) = f (u) + f (v) for all edges uv such thatfor all a and b in A, |v f (a) -v f (b)| ≤ 1 and the induced edge labels are 2, 4,..., 2q where v f (a) be the number of vertices v with f (v) = a for a ∈ A. A graph that admits odd vertex equitable even labeling is called odd vertex equitable even graph. We investigate the odd vertex equitable even behavior of some standard graphs.<![CDATA[<strong>Yet another variant of the Drygas functional equation on groups</strong>]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000100002&lng=pt&nrm=iso&tlng=pt
Let G be a group and C the field of complex numbers. Suppose σ1,σ 2 : G → G are endomorphisms satisfying the condition σi(σi(x)) = x for all x in G and for i = 1, 2. In this paper, we find the central solution f : G → C of the equation f (xy) + f (σi(y)x) =2f (x) + f (y) + f (σ2(y)) for all x,y ∈ G which is a variant of the Drygas functional equation with two involutions. Further, we present a generalization the above functional equation and determine its central solutions. As an application, using the solutions ofthe generalized equation, we determine the solutions f, g, h, k : GxG → C ofthefunc-tional equation f (pr, qs) + g(sp, rq) = 2f (p, q) + h(r, s) + k(s, r) when f satisfies the condition f (pr, qs) = f (rp, sq) for all p, q, r, s ∈ G.<![CDATA[<strong>On the hyperstability of a quartic functional equation in Banach spaces</strong>]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000100003&lng=pt&nrm=iso&tlng=pt
In this paper, we establish some hyperstability results of the following functional equation f (2x + y) + f (2x - y) = 4(f (x + y) + f (x - y)) + 24f (x) - 6f (y) in Banach spaces.<![CDATA[<strong>Generalizations of Hermite-Hadamard and Ostrowski type inequalities for MT<sub>m</sub>-preinvex functions</strong>]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000100004&lng=pt&nrm=iso&tlng=pt
In the present paper, the notion of MTm-preinvex function is introduced and some new integral inequalities involving MTm-preinvex functions along with beta function are given. Moreover, some generalizations of Hermite-Hadamard and Ostrowski type inequalities for MTm-preinvexfunctions via classical integrals and Riemann-Liouville fractional integrals are established. These results not only extends the results appeared in the literature (see [10], [11], [12]), but also provide new estimates on these types.<![CDATA[<strong>A weakened version of Davis-Choi-Jensen’s inequality for normalised positive linear maps</strong>]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000100005&lng=pt&nrm=iso&tlng=pt
In this paper we show that the celebrated Davis-Choi-Jensen’s inequality for normalised positive linear maps can be extended in a weakened form for convex functions. A reverse inequality and applications for important instances of convex (concave) functions are also given.<![CDATA[<strong>Spectral properties of horocycle flows for compact surfaces of constant negative curvature</strong>]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000100006&lng=pt&nrm=iso&tlng=pt
We consider flows, called Wu flows, whose orbits are the unstable manifolds of a codimension one Anosov flow. Under some regularity assumptions, we give a short proof of the strong mixing property of Wu flows and we show that Wu flows have purely absolutely continuous spectrum in the orthocomplement of the constant functions. As an application, we obtain that time changes of the classical horocycle flows for compact surfaces of constant negative curvature have purely absolutely continuous spectrum in the orthocomplement of the constant functions for time changes in a regularity class slightly less than C². This generalises recent results on time changes ofhorocycle flows.<![CDATA[<strong>Some I-convergent triple sequence spaces defined by a sequence of modulus function</strong>]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000100007&lng=pt&nrm=iso&tlng=pt
In this article we introduce the notion of I-convergent triple sequence spaces cOI³(F), cI³(F), l00I³(F), mI³(F) and mOI³(F) defined by a sequence of modulii F = (f pqr) and study some of their algebraic and topological properties like solidity, symmetricity, convergence free etc. We also prove some inclusion relation involving these sequence spaces.<![CDATA[<strong>Representation fields for orders of small rank</strong>]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000100008&lng=pt&nrm=iso&tlng=pt
A representation field for a non-maximal order H in a central simple algebra is a subfield of the spinor class field of maximal orders which determines the set of spinor genera of maximal orders representing H. In our previous work we have proved the existence of the representation field for several important families of suborders, like commutative orders, while we have also found examples where the representation field fails to exist. To be precise, we have found full-rank orders, in central simple algebras of dimension 9 or larger over a suitable field, whose representation field is undefined. In this article, we prove that the representation field is defined for any order H of rank r < 7. This is done by defining representation fields for arbitrary representations of orders into central simple algebra and showing that the computation of these generalized representation fields can be reduced to the case of irreducible representations. The same technique yields the existence of representation fields for any order in an algebra whose semi-simple reduction is commutative. We also construct a rank-8 order, in a 16-dimensional matrix algebra, whose representation field is not defined.<![CDATA[<strong>Strong right fractional calculus for Banach space</strong> <strong>valued functions</strong>]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000100009&lng=pt&nrm=iso&tlng=pt
We present here a strong right fractional calculus theory for Banach space valued functions of Caputo type. Then we establish many right fractional Bochner integral inequalities of various types.<![CDATA[<strong>Jensen’s and the quadratic functional equations with an endomorphism</strong>]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000100010&lng=pt&nrm=iso&tlng=pt
We determine the solutions f : S → H of the generalized Jensen’s functional equation f (x + y) + f (x + φ(y)) = 2f (x), x,y ∈ S, and the solutions f : S → H of the generalized quadratic functional equation f (x + y) + f (x + φ(y)) = 2f (x) + 2f (y), x,y ∈ S, where S is a commutative semigroup, H is an abelian group (2-torsion free in the first equation and uniquely 2-divisible in the second) and φ is an endomorphism of S.