Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the Lebedev-Milin inequality


Author: Mishael Zedek
Journal: Proc. Amer. Math. Soc. 33 (1972), 395-397
MSC: Primary 30A04
DOI: https://doi.org/10.1090/S0002-9939-1972-0294608-7
MathSciNet review: 0294608
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A generalization is given of an inequality of Lebedev-Milin involving the coefficients of a power series f and those of $ \exp (f)$. It is proved that the exponential function can be replaced by certain, functions belonging to the family of functions whose Taylor expansions at the origin have nonnegative coefficients.


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

  • [1] Dov Aharonov, On Bieberbach Eilenberg functions, Bull. Amer. Math. Soc. 76 (1970), 101-104. MR 41 #1994. MR 0257343 (41:1994)
  • [2] L. P. Il'ina, The relative growth of nearby coefficients of schlicht functions, Mat. Zametki 4 (1968), 715-722. (Russian) MR 39 #1644. MR 0240295 (39:1644)
  • [3] N. A. Lebedev and I. M. Milin, An inequality, Vestnik Leningrad. Univ. 20 (1965), no. 19, 157-158. (Russian) MR 32 #4248. MR 0186793 (32:4248)
  • [4] I. M. Milin, Estimation of coefficients of univalent functions, Dokl. Akad. Nauk SSSR 160 (1965), 769-771 = Soviet Math. Dokl. 6 (1965), 196-198. MR 30 #3206. MR 0172991 (30:3206)
  • [5] Z. Nehari, On the coefficients of Bieberbach-Eilenberg functions, J. Analyse Math. 23 (1970), 297-303. MR 0273003 (42:7884)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30A04

Retrieve articles in all journals with MSC: 30A04


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0294608-7
Keywords: Lebedev-Milin inequalities, coefficient inequalities, univalent functions, Bieberbach-Eilenberg functions
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society