The Fekete-Szegő problem for strongly 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 Komatu Integral Operator and Strongly Close-to-convex Functions

In this paper we introduce some new subclasses of strongly closeto-convex functions de…ned by using the Komatu integral operator and study their inclusion relationships with the integral preserving properties. Theorem[section] [theorem]Lemma [theorem]Proposition [theorem]Corollary Remark

On the quadratic support of strongly convex functions

In this paper, we first introduce the notion of $c$-affine functions for $c> 0$. Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.

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