In this article, we introduce and study a new family P?(?,?,k,?,?,?,r) of normalized analytic ?-pseudo-starlike bi-univalent functions by using the Horadam polynomials, which is associated with certain convolution operator defined in open unit disk U. We establish bounds for |a2| |a3|, where a2, a3 are initial Taylor-Maclaurin coefficients. Furthermore, obtain Fekete-Szeg? inequality class P? (...

is finite. Assume that the analytic function u(r, x) can be continued across some arc of the boundary of the unit circle. Then the ak are equal, beyond some point, to the terms of a periodic sequence. A number of generalizations and related results have been published [2; 3; 4; 5; 9], of which we mention in particular that of Duffin and Schaeffer [4]; these authors replace the hypothesis that u...

Tensor products of Gauss-Lobatto quadrature points are frequently used as collocation points in spectral element methods. Unfortunately, it is not known if Gauss-Lobatto points exist in non-tensor-product domains like the simplex. In this work, we show that the n-dimensional tensor-product of Gauss-Lobatto quadrature points are also Fekete points. This suggests a way to generalize spectral meth...

In this paper, we find Fekete-Szegö bounds for a generalized class M q (γ, φ). Also, we discuss some remarkable results.

A classical theorem of Fekete and Szegő [4] says that if E is a compact set in the complex plane, stable under complex conjugation and having logarithmic capacity γ(E) ≥ 1, then every neighborhood of E contains infinitely many conjugate sets of algebraic integers. Raphael Robinson [5] refined this, showing that if E is contained in the real line, then every neighborhood of E contains infinitely...

Michael J. Szego,* Janet A. Buchanan, and Stephen W. Scherer,,**, *The Centre for Clinical Ethics, Toronto, ON M6R 1B5, Canada, †The Centre for Applied Genomics, The Hospital for Sick Children, Toronto, ON M5G 1X8, Canada, ‡The Joint Centre for Bioethics, University of Toronto, Toronto, ON M5T 1P8, Canada, §Program in Genetics and Genome Biology, The Hospital for Sick Children, Toronto, ON M5G ...