It is well known that (see [9]) Cesaro means of 2π-periodic functions f ∈ Lp(T) (1 ≤ p ≤ ∞) converges by norms. Hereby T is denoted the interval (−π,π). The problem of the mean summability in weighted Lebesgue spaces has been investigated in [6]. A 2π-periodic nonnegative integrable function w : T→R1 is called a weight function. In the sequel by L p w(T), we denote the Banach function space of ...

In the paper Gaussian curvature of Bergman metric on the unit disc and the dependence of this curvature on the weight function has been studied.

In this paper we obtain the bound on the average sensitivity of the weighted sum function. This confirms a conjecture of Shparlinski. We also compute the weights of the weighted sum functions and show that they are almost balanced.

We investigate the existence of positive principal eigenvalues of the problem —Au(x) = lg(x)u for x e R" ; u(x) —* 0 as x —> oo where the weight function g changes sign on R" . It is proved that such eigenvalues exist if g is negative and bounded away from 0 at oo or if n > 3 and \g(x)\ is sufficiently small at oo but do not exist if n = 1 or 2 and fRn g(x)dx > 0 .

This article introduces a discount parameter and a weight function in Myerson’s (1977) classical model of cooperative games with restrictions on cooperation. The discount parameter aims to reflect the time preference of the agents while the weight function aims to reflect the importance of each node of a graph. We provide axiomatic characterizations of two types of solution that are inspired by...

Let X be a finite set with n elements. A function f : X −→ R such that ∑ x∈X f (x) ≥ 0 is called a n-weight function. In 1988 Manickam and Singhi conjectured that, if d is a positive integer and f is a n-weight function with n ≥ 4d there exist at least (n−1 d−1 ) subsets Y of X with |Y | = d for which ∑ y∈Y f (y) ≥ 0. In this paper we study this conjecture and we show that it is true if f is a ...

A 2-rainbow dominating function ( ) of a graph  is a function  from the vertex set  to the set of all subsets of the set  such that for any vertex  with  the condition  is fulfilled, where  is the open neighborhood of . A maximal 2-rainbow dominating function on a graph  is a 2-rainbow dominating function  such that the set is not a dominating set of . The weight of a maximal    is the value . ...