Let be the class of analytic functions in the unit disk that are normalized with f (0)= f ′(0)− 1 = 0 and let −1 ≤ B < A ≤ 1. In this paper we study the class Gλ,α = { f ∈ : |(1− α + αz f (z)/ f ′(z))/z f ′(z)/ f (z)− (1− α)| < λ, z ∈ }, 0 ≤ α ≤ 1, and give sharp sufficient conditions that embed it into the classes S∗[A,B] = { f ∈ : z f ′(z)/ f (z) ≺ (1 +Az)/(1 + Bz)} and K(δ) = { f ∈ : 1 + z f...

Sharp bounds for japþ2 lapþ1j and jap+3j are derived for certain p-valent analytic functions. These are applied to obtain Fekete-Szegö like inequalities for several classes of functions defined by convolution. 2006 Elsevier Inc. All rights reserved.

which are analytic in the open unit disk U {z : z ∈ C and |z| < 1} and S denote the subclass ofA that are univalent in U. A function f z inA is said to be in class S∗ of starlike functions of order zero in U, if R zf ′ z /f z > 0 for z ∈ U. Let K denote the class of all functions f ∈ A that are convex. Further, f is convex if and only if zf ′ z is star-like. A function f ∈ A is said to be close...

Suppose that K ⊂ IR is either the unit ball, the unit sphere or the standard simplex. We show that there are constants c1, c2 > 0 such that for a set of Fekete points (maximizing the Vandermonde determinant) of degree n, Fn ⊂ K, c1 n ≤ min b∈Fn b 6=a dist(a, b) ≤ c2 n , ∀a ∈ Fn where dist(a, b) is a natural distance on K that will be described in the text. §

In this paper we present a procedure for the numerical estimation of the Fekete points of a wide variety of compact sets in IR. We understand the problem of the Fekete points in terms of the identification of nearly equilibrium configurations for a potential energy that depends on the relative position of N particles. The compact sets for which our procedure has been designed can be described b...

Sprawozdanie przygotowane/finansowane w ramach programu Ministra Nauki i Szkolnictwa Wy?szego pod nazw? DIALOG latach 2019–2021. Jest wynikiem udzia?u projekcie badawczym pt. „O?rodek bada? historii kobiet”, nr 0016/DLG/2019/10.

Introduction. In 1923 M. Fekete [2]2 introduced the concept of factor sequences that left invariant the class of a Fourier series. That is, Fekete investigated the conditions to which a sequence of constants (X„) must be subjected in order that (X„a„, X„i„) be Fourier coefficients of a function of the same class, K, as that of the function determined by (an, bn). Whenever (X„) has this property...

The two-dimensional orthogonal non-guillotine cutting problem (NGCP) appears in many industries (like wood and steel industries) and consists in cutting a rectangular master surface into a number of rectangular pieces, each with a given size and value. The pieces must be cut with their edges always parallel or orthogonal to the edges of the master surface (orthogonal cuts). The objective is to ...

Locating good points for multivariate polynomial approximation, in particular interpolation, is an open challenging problem, even in standard domains. One set of points that is always good, in theory, is the so-called Fekete points. They are defined to be those points that maximize the (absolute value of the) Vandermonde determinant on the given compact set. However, these are known analyticall...