On the Fekete-Szegö problem for strongly \(\alpha\)-logarithmic quasiconvex functions
type: Item
instance of: scholarly article
title: On the Fekete-Szegö problem for strongly \(\alpha\)-logarithmic quasiconvex functions
zbMATH Open document ID: 1086.30011
published in: Southeast Asian Bulletin of Mathematics
publication date: 2005-03-11T00:00:00Z
review text: Let \(S\) denote the class of normalized analytic functions, which are univalent in the open unit disk of the form \(f(z)= z+ \sum^\infty_{n=2} a_n z^n\), \(n= 1,2,\dots\). A classical result of M. Fekete and G. Szegő is the following sharp inequality for \(f\in S\) \[ |a_3-\mu a^2_2|\leq \begin{cases} 3- 4\mu\quad &\text{if }\mu\leq 0,\\ 1+ 2e^{-2\mu/(1- \mu)}\quad &\text{if }0\leq \mu\leq 1,\\ 4\mu- 3\quad &\text{if }\mu\geq 1.\end{cases} \] In this paper the authors introduce new subclasses of \(S\), called normalized strongly \(\alpha\)-logarithmic convex and quasiconvex functions of order \(\beta\) and obtain sharp Fekete-Szegő inequalities for functions belonging to this classes.
reviewed by: O. Fekete
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 2144204
zbMATH Keywords: Fekete-Szegő problem
zbMATH Keywords: convex quasiconvex
zbMATH Keywords: strongly \(\alpha\)-logarithmic convex
author: Nak Eun Cho
author: Shigeyoshi Owa
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2144204