On the Fekete-Szegő problem for close-to-convex functions

On the Fekete-Szeg6 problem for close-to-convex functions II

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...

The Fekete – Szegő theorem with splitting conditions : Part

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...

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points

The Fekete-Szegö Problem for p-Valently Janowski Starlike and Convex Functions

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.

Fekete-Szegő Inequality for a Subclass of p-Valent Analytic Functions

which are analytic in the open unit disk E. Also, A1 = A, the usual class of analytic functions defined in the open unit disk E = {z : |z| < 1}. Let f(z) and g(z) be analytic in E. We say that the function f is subordinate to the function g and write f(z) ≺ g(z), if and only if there exists Schwarz function w, analytic in E such that w(0) = 0, |w(z)| < 1 for z ∈ E, and f(z) = g(w(z)). In partic...