In the present paper, sharp upper bounds of |a3 −μa2| for the functions f(z) = z + a2z + a3z + · · · belonging to a new subclass of Sakaguchi type functions are obtained. Also, application of our results for subclass of functions defined by convolution with a normalized analytic function are given. In particular, Fekete-Szegö inequalities for certain classes of functions defined through fractio...

We propose a numerical method (implemented in Matlab) for computing algebraic quadrature nodes and weights on compact multivariate domains. It relies on the search of maximum volume submatrices of Vandermonde matrices in suitable polynomial bases, by a greedy algorithm based on QR factorization with column pivoting. Such nodes are approximate Fekete points, and are good also for polynomial inte...

It is shown that a conjecture of E.A. Rakhmanov is true concerning the zero distribution of orthogonal polynomials with respect to a measure having a discrete real support. We also discuss the case of extremal polynomials with respect to some discrete L p {norm, 0 < p 1, and give an extension to complex supports. Furthermore, we present properties of weighted Fekete points with respect to discr...

We prove a formula for the Fekete-Leja transfinite diameter of the pullback of a set E ⊂ C by a regular polynomial map F , expressing it in terms of the resultant of the leading part of F and the transfinite diameter of E. We also establish the nonarchimedean analogue of this formula. A key step in the proof is a formula for the transfinite diameter of the filled Julia set of F .

We investigate large sieve inequalities such as 1 m m X j=1 log P e j C 2 Z 2 0 log e P e d ; where is convex and increasing, P is a polynomial or an exponential of a potential, and the constant C depends on the degree of P , and the distribution of the points 0 1 < 2 < < m 2 . The method allows greater generality and is in some ways simpler than earlier ones. We apply our results to estimate t...

The purpose of this paper is to study the coefficient estimates class functions in ()consisting starlike functions. sharp upper bounds for initial coefficients and Fekete-Szego functional were established using Opoola Differential Operator