Volume 62, Issue 1

The betweenness centrality of a vertex of a graph is the portion of the shortest paths between all pairs of vertices passing through a given vertex. We study upper bounds for this invariant and its relations to the diameter and average distance of a graph.

A connection between sums $\sum\limits_{k \equiv j(\bmod p)} {( - 1)^k (_k^{np^m } )} $ and Gross-Koblitz formula is given.

Our objective here is to prove that the uniform convergence of a sequence of Kurzweil integrable functions implies the convergence of the sequence formed by its corresponding integrals.

For analytic functions f(z) in the open unit disk U and convex functions g(z) in U, Nunokawa et al. [NUNOKAWA, M.—OWA, S.—NISHIWAKI, J.—KUROKI, K.—HAYAMI, T: Differential subordination and argumental property, Comput. Math. Appl. 56 (2008), 2733–2736] have proved one theorem which is a generalization of the result [POMMERENKE, CH.: On close-toconvex analytic functions, Trans. Amer. Math. Soc. 114 (1965), 176–186]. The object of the present paper is to generalize the theorem due to Nunokawa et al..

In this paper, we discuss the uniqueness of meromorphic functions concerning fixed points. In view of the fixed points, we extend a recent conclusion due to Zhang and Lin. Moreover, under the condition of f and g sharing ∞ IM, our theorem generalizes some previous results of Fang and Qiu, Lin and Yi and so on.

In this paper, we firstly give a new definition, namely, the T point of algebroid functions. Then by using Ahlfors’ theory of covering surfaces, we prove the existence of these points for any ν-valued algebroid functions in the unit disk satisfying $\mathop {\lim \sup }\limits_{r \to 1^ - } \frac{{T(r,w)}} {{\log \tfrac{1} {{1 - r}}}} = + \infty $. This extends the recent results of Xuan, Wu and Sun.

An interesting generalization of statistical convergence is I-convergence which was introduced by P.Kostyrko et al [KOSTYRKO,P.—ŠALÁT,T.—WILCZYŃSKI,W.: I-Convergence, Real Anal. Exchange 26 (2000–2001), 669–686]. In this paper, we define and study the concept of I-convergence, I*-convergence, I-limit points and I-cluster points in probabilistic normed space. We discuss the relationship between I-convergence and I*-convergence, i.e. we show that I*-convergence implies the I-convergence in probabilistic normed space. Furthermore, we have also demonstrated through an example that, in general, I-convergence does not imply I*-convergence in probabilistic normed space.

In this paper, we introduce a class of linear positive operators based on q-integers. For these operators we give some convergence properties in weighted spaces of continuous functions and present an application to differential equation related to q-derivatives. Furthermore, we give a Stancu-type remainder.

An inverse theorem of the trigonometric approximation theory in Weighted Orlicz spaces is proved and the constructive characterization of the generalized Lipschitz classes defined in these spaces is obtained.

We introduce certain generalized Szász-Mirakyan operators in exponential weight spaces of functions of two variables and we give approximation theorems for them.

The purpose of this paper is to introduce and study the concepts of double $\bar \lambda $-statistically convergent and double $\bar \lambda $-statistically Cauchy sequences in probabilistic normed space.

We consider the notion of real center of mass and total center of mass of a bounded linear operator relative to another bounded linear operator and explore their relation with cosine and total cosine of a bounded linear operator acting on a complex Hilbert space. We give another proof of the Min-max equality and then generalize it using the notion of orthogonality of bounded linear operators. We also illustrate with examples an alternative method of calculating the antieigenvalues and total antieigenvalues for finite dimensional operators.

In this paper, a generalized vector equilibrium problem is introduced and studied. A scalar characterization of weak efficient solutions for the generalized vector equilibrium problem is obtained. By using the scalarization result, the existence of the weak efficient solutions and the connectedness of the set of weak efficient solutions for the generalized vector equilibrium problem are proved in locally convex spaces.

We define and study the notions of pseudovariant maps and pseudogeny maps on G-spaces. We prove that the set of all pseudogenies of a locally comapct G-space is a group. We further obtain representation of pseudovariant maps in terms of pseudogenies. Finally, we obtain Tietze type extension result for pseudovariant homotopies defined on locally compact second countable G-spaces.

In certain settings the mean response is modeled by a linear model using a large number of parameters. Sometimes it is desirable to reduce the number of parameters prior to conducting the experiment and prior to the actual statistical analysis. Essentially, it means to formulate a simpler approximate model to the original “ideal” one. The goal is to find conditions (on the model matrix and covariance matrix) under which the reduction does not influence essentially the data fit. Here we try to develop such conditions in regular linear model without and with linear restraints. We emphasize that these conditions are independent of observed data.