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

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Coefficients and integral means of some classes of analytic functions


Author: T. Sheil-Small
Journal: Proc. Amer. Math. Soc. 88 (1983), 275-282
MSC: Primary 30C45; Secondary 30C50
MathSciNet review: 695258
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The sharp coefficient bounds for the classes $ {V_k}$ of functions of bounded boundary rotation are obtained by a short and elementary argument. Elementary methods are also applied for the coefficients of related classes characterised by a generalised Kaplan condition. The result $ {(1 + xz)^\alpha }{(1 - z)^{ - \beta }} \ll {(1 + z)^\alpha }{(1 - z)^{ - \beta }}$ $ (\left\vert x \right\vert = 1,\alpha \geqslant 1,\beta \geqslant 1)$ is proved simply. It is further shown that the functions $ {(1 + z)^\alpha }{(1 - z)^{ - \beta }}$ are extremal for the $ p$th means ($ p$ an arbitrary real) of all Kaplan classes $ K(\alpha ,\beta )$.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30C45, 30C50

Retrieve articles in all journals with MSC: 30C45, 30C50


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0695258-8
PII: S 0002-9939(1983)0695258-8
Keywords: Functions of bounded boundary rotation, starlike functions, close-to-convex functions
Article copyright: © Copyright 1983 American Mathematical Society