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On the quotient of the representations of convexity and starlikeness

✍ Scribed by Nikola Tuneski

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 102 KB
Volume: 248-249
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200310015

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✦ Synopsis

Abstract

Let f(z) = z + a~2~z^2^ + … be an analytic function in the unit disk 𝒰 = {z : |z| < 1}. Such a function belongs to the class G~b~ defined by Silverman if the quotient of the analytic representations of convexity and starlikeness of the function maps the unit disk into a disk with center 1 and radius b. By using the Jack lemma we analyze the relation between the class G~b~ and the class S*[A,B] and its subclasses.

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