An application of Miller and Mocanu's result
type: Item
instance of: scholarly article
title: An application of Miller and Mocanu's result
zbMATH Open document ID: 0709.30008
DOI: 10.1155/S0161171290000874
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46520
review text: For a fixed c and for an analytic f(z), \(f(0)=f'(0)-1=0\), \(| z| <1\), the operator \(I_ c(f)\) is defined by the formula \[ I_ c(f)=(1+c)z^{-c}\int^{z}_{0}t^{-c}f(t)dt. \] It is known that if Re\(\{\) \(c\}\geq 0\) and f(z) is starlike then \(I_ c(f)\) is also starlike [\textit{Z. Lewandowski}, \textit{S. Miller} and the reviewer, Proc. Am. Math. Soc. 56, 111-117 (1976; Zbl 0298.30008)]. In this note it is shown that if f(z) is analytic, \(c>-1\) and some complicated conditions are met then \(| I_ c(f)| <1\).
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 4165241
author: Shigeyoshi Owa
author: Zhwo-Ren Wu
reviewed by: Eligiusz Złotkiewicz
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4165241