On the line and its tensor products, Fekete points are known to be the Gauss–Lobatto quadrature points. But unlike high-order quadrature, Fekete points generalize to non-tensor-product domains such as the triangle. Thus Fekete points might serve as an alternative to the Gauss–Lobatto points for certain applications. In this work we present a new algorithm to compute Fekete points and give resul...

In this present investigation, the authors obtain Fekete-Szegö’s inequality for certain normalized analytic functions f(z) defined on the open unit disk for which zf ′(z)+αz2f ′′(z) (1−α)f(z)+αzf ′(z) (α ≥ 0) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by convolution are...

where the coefficients are Legendre symbols, is called the p-th Fekete polynomial. In this paper the size of the Fekete polynomials on subarcs is studied. We prove essentially sharp bounds for the average value of |fp(z)| , 0 < q < ∞, on subarcs of the unit circle even in the cases when the subarc is rather small. Our upper bounds are matching with the lower bounds proved in a preceding paper f...

Giving a (partial) solution to a problem of S. Fekete [3] and S. Fekete and G.J. Woeginger [4] we show that given a finite set X of points in the plane, it is possible to find a polygonal path with |X|−1 segments and with vertex set X so that every angle on the polygonal path is at least π/9. According to a conjecture of Fekete and Woeginger, π/9 can be replaced by π/6. Previously, the result h...

For p-valently Janowski starlike and convex functions defined by applying subordination for the generalized Janowski function, the sharp upper bounds of a functional |a p2 − μa 2 p1 | related to the Fekete-Szegö problem are given.

For non-zero complex b, let N b m,n(φ) (m > n), m ∈ N, n ∈ N0 denote the class of normalized univalent functions f satisfying 1+ 1 b ( Df(z) Dnf(z) − 1 ) ≺ φ(z), z in the open unit disk U , where Dnf denotes the Sălăgean derivative of f . In this paper, we obtain sharp bounds for the Fekete-Szegö functional |a3 − μa2|.

In this communication we present a new method to estimate Fekete points on surfaces. Our method works in a general setting, in the sense that we can obtain good estimations of the Fekete points on piecewise regular surfaces. The determination of Fekete points in the unit sphere is considered as a model of a highly non-linear optimization problem with non-linear constraints. In fact, obtaining a...

Let E be a compact set in C with connected complement and positive logarithmic capacity. For any f continuous on E and analytic in the interior of E, we consider the distribution of extreme points of the error of best uniform polynomial approximation on E. Let Λ = (nj) be a subsequence of N such that nj+1/nj → 1. If, for n ∈ Λ, An(f) ⊆ ∂E denotes the set of extreme points of the error function,...

Virtual environments have shown great promise as a research tool in science and engineering. In this paper we study a classical problem in mathematics: that of approximating globally optimal Fekete point configurations. We found a highly interactive virtual environment, combined with a time-critical computation, can provide valuable insight into the symmetry and stability of Fekete point config...

The Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of the Fekete points in the sphere. The way we proceed is by showing their connection with other array of points, the Marcinkiewicz-Z...