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...

The zeros of semi-orthogonal functions with respect to a probability measure µ supported on the unit circle can be applied to obtain Szeg˝ o quadrature formulas. The discrete measures generated by these formulas weakly converge to the orthogonality measure µ. In this paper we construct families of semi-orthogonal functions with interlacing zeros, and give a representation of the support of µ in...

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|.

Let C (fl), fl > 0, denote the family of no rmal i zed c loseto-convex funct ions of o rder ft. F o r fl = 1 this is the usual set of c loseto-convex functions, which had been defined by Kap lan . In a prev ious pape r [3] we solved the Fekete-Szeg6 p r o b l e m of maximiz ing l a 3 2 a2l, 2 ~ [0, 1], for c loseto-convex functions. The largest n u m b e r 20 for which [a a 20 a2[ is max imized...

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...

This manuscript presents Hyers-Ulam stability and Hyers--Ulam--Rassias stability results of non-linear Volterra integro--delay dynamic system on time scales with fractional integrable impulses. Picard fixed point theorem  is used for obtaining  existence and uniqueness of solutions. By means of   abstract Gr"{o}nwall lemma, Gr"{o}nwall's inequality on time scales, we establish  Hyers-Ulam stabi...

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,...