Proyecciones (Antofagasta)

Companions of Hermite-Hadamard Inequality for Convex Functions (II)

Companions of Hermite-Hadamard inequalities for convex functions defined on the positive axis in the case when the integral has either the weight ψ or ¹ ,t > 0 are given. Applications for special means are provided as well.

L(1,1)-Labeling of Direct Product of any Path and Cycle

Suppose that [n] = {0, 1, 2,...,n} is a set of non-negative integers and h,k G [n].The L (h, k)-labeling of graph G is the function l : V(G) - [n] such that |l(u) - l(v)| > h if the distance d(u,v) between u and v is 1 and |l(u) - l(v)| > k if d(u,v) = 2. Let L(V(G)) = {l(v): v G V(G)} and let p be the maximum value of L(V(G)). Then p is called Xi^-number of G if p is the least possible member of [n] such that G maintains an L(h, k) - labeling. In this paper, we establish X} - numbers of Pm X Pn and Pm X Cn graphs for all m,n > 2.

The upper open monophonic number of a graph

For a connected graph G of order n,a subset S of vertices of G is a monophonic set of G if each vertex v in G lies on a x-y monophonic path for some elements x and y in S. The minimum cardinality of a monophonic set of G is defined as the monophonic number of G, denoted by m(G). A monophonic set of cardinality m(G) is called a m-set of G.A set S of vertices of a connected graph G is an open monophonic set of G if for each vertex v in G ,either v is an extreme vertex of G and v G S,or v is an internal vertex of a x-y mono-phonic path for some x,y G S. An open monophonic set of minimum cardinality is a minimum open monophonic set and this cardinality is the open monophonic number, om(G). An open monophonic set S of vertices in a connected graph G is a minimal open monophonic .set if no proper subset of S is an open monophonic set of G.The upper open monophonic number om+ (G) is the maximum cardinality of a minimal open monophonic set of G. The upper open monophonic numbers of certain standard graphs are determined. It is proved that for a graph G of order n, om(G) = n if and only if om+(G)= n. Graphs G with om(G) = 2 are characterized. If a graph G has a minimal open monophonic set S of cardinality 3, then S is also a minimum open monophonic set of G and om(G) = 3. For any two positive integers a and b with 4 < a < b, there exists a connected graph G with om(G) = a and om+(G) = b.

On linear maps that preserve G-partial-isometries in Hilbert space

Let Ti be a complex Hilbert space and B(TT) the algebra of all bounded linear operators on H. We give the concrete forms of surjec-tive continue unital linear maps from B(TT) onto itself that preserves G-partial-isometric operators.

Fróchet differentiation between Menger probabilistic normed spaces

In this paper, we define and study Menger weakly and strongly P-convergent sequences and then Menger probabilistic continuity. We also display Frechet differentiation of nonlinear operators between Menger probabilistic normed spaces.

Difference sequence spaces in cone metric space

In this article we introduce the notion of difference bounded, convergent and null sequences in cone metric space. We investigate their different algebraic and topological properties.

Subseries convergence in abstract duality pairs

Let E, F be sets, G an Abelian topological group and b : ExF - G. Then (E, F, G) is called an abstract triple. Let w(F, E) be the weakest toplogy on F such that the maps {b(x, ·): x G E} from F into G are continuous. A subset B C F is w(F,E) sequentially conditionally compact if every sequence {yk} C B has a subsequence {y nk } such that limj; b(x, y nk) exists for every x G E. It is shown that if a formal series in E is subseries convergent in the sense that for every subsequence {x nj} there is an element x G E such that Xj=! b(x nj ,y) = b(x,y) for every y G F ,then the series Xj=! b(x nj ,y) converge uniformly for y belonging to w(F, E) sequentially conditionally compact subsets ofF. This result is used to establish Orlicz-Pettis Theorems in locall convex and function spaces. Applications are also given to Uniform Boundedness Principles and continuity results for bilinear mappings.

Topological indices of Kragujevac trees

We find the extremal values of the energy, the Wiener index and several vertex-degree-based topological indices over the set of Kragujevac trees with the central vertex of fixed degree.