Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


On some starlike and convex functions

Author: G. M. Shah
Journal: Trans. Amer. Math. Soc. 154 (1971), 83-91
MSC: Primary 30.42
MathSciNet review: 0269826
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we study functions of the form $ \smallint _0^z(g(t)/\Pi _{k = 1}^n{(1 - t{z_k})^{{\alpha _k}}})$ for $ \vert z\vert < 1$ and show under what conditions such a function is convex, convex in one direction and hence univalent in $ \vert z\vert < 1$. We also study the functions $ g(z)$ where $ g(0) = 1,g(z) \ne 0$ and $ \operatorname{Re} \;[zg'(z)/g(z)] \geqq - \alpha ,0 \leqq \alpha < 1$, for $ \vert z\vert < 1$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 30.42

Retrieve articles in all journals with MSC: 30.42

Additional Information

PII: S 0002-9947(1971)0269826-8
Keywords: Univalent, starlike, convex, Schwarz-Christoffel transformation, Herglotz's representation, extremal functions, contour
Article copyright: © Copyright 1971 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia