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...

A new class of multivalent holomorphic functions with complex order in terms of subordination is introduced. We find some properties of this class like, sufficient coefficient bound, integral operator and Feketo-Szego problem. AMS Mathematics Subject Classification (2000): Primary 30C45; Secondary 30C80

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...

We discuss and compare two greedy algorithms, that compute discrete versions of Fekete-like points for multivariate compact sets by basic tools of numerical linear algebra. The first gives the so-called “Approximate Fekete Points” by QR factorization with column pivoting of Vandermonde-like matrices. The second computes Discrete Leja Points by LU factorization with row pivoting. Moreover, we st...

The objective of this work is to provide a methodology for approximating globally optimal Fekete point con-gurations. This problem is of obvious interest in numerical mathematics and scientic modeling. Following a brief discussion of the pertinent analytical background, Lipschitz global optimization (LGO) is applied to determine {i.e., to numerically approximate{ Fekete point congurations. Next...

Let $\mathcal{S}^{\ast}_{L}(\lambda)$ be the class of functions $f$, analytic in unit disc $\Delta=\{z:|z|<1\}$, with normalization $f(0)=f'(0)-1=0$, which satisfy condition\begin{equation*}\frac{zf'(z)}{f(z)}\prec \left(1+z\right)^{\lambda},\end{equation*}where $\prec$ is subordination relation. The a subfamily known strongly starlike order $\lambda$. In this paper,the relations between and...