p-valent classes related to convex functions of complex order
type: Item
instance of: scholarly article
title: p-valent classes related to convex functions of complex order
zbMATH Open document ID: 0587.30021
DOI: 10.1216/RMJ-1985-15-4-853
author: M. K. Aouf
published in: Rocky Mountain Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: Let C(b,p) (b\(\neq 0\) complex, \(p\geq 1\) integer) denote the class of functions \(f(z)=z^ p+a_{p+1}z^{p+1}+...\). which are regular in the unit disc U and such that \[ Re\{p+(1/b)(1-p+zf'(z)/f(z))\}>0\quad for\quad z\in U. \] In this paper the representation formula \[ f(z)=pz^{p-1} \exp \{-2bp\int^{2p}_{0}\log (1-ze^{-it})d\mu (t) \] and the estimations of the modulus of the derivative and the coefficients for the functions of the class C(b,p) are given. In the special cases C(1,1), C(b,1), C(1,p) we obtain the known subclasses of regular functions.
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 30C50
zbMATH DE Number: 3941875
zbMATH Keywords: p-valent functions
reviewed by: Jan Stankiewicz
MaRDI profile type: Publication
full work available at URL: rmj-1985-15-4-853
OpenAlex ID: W2020361209
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description: scientific article; zbMATH DE number 3941875