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)

 
 

 

A coefficient inequality for convex univalent functions


Author: S. Y. Trimble
Journal: Proc. Amer. Math. Soc. 48 (1975), 266-267
DOI: https://doi.org/10.1090/S0002-9939-1975-0355027-0
MathSciNet review: 0355027
Full-text PDF Free Access

Abstract | References | Additional Information

Abstract: A short proof of $ \vert a_2^2 - {a_3}\vert \leq (1 - \vert{a_2}{\vert^2})/3$ is given for normalized convex univalent functions.


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

  • [1] J. A. Hummel, The coefficient regions of starlike functions, Pacific J. Math. 7 (1957), 1381-1389. MR 20 #1780. MR 0095274 (20:1780)
  • [2] F. R. Keogh and E. P. Merkes, A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc. 20 (1969), 8-12. MR 38 #1249. MR 0232926 (38:1249)
  • [3] Z. Nehari, Conformal mapping, McGraw-Hill, New York, 1952. MR 13, 640. MR 0045823 (13:640h)
  • [4] M. S. Robertson, Univalent functions $ f(z)$ for which $ zf'(z)$ is spirallike, Michigan Math. J. 16 (1969), 97-101. MR 39 #5785. MR 0244471 (39:5785)
  • [5] J. Szynal, Some remarks on coefficients inequality for $ \alpha $-convex functions, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 20 (1972), 917-919. MR 47 #454. MR 0311892 (47:454)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0355027-0
Keywords: Convex univalent functions, coefficient inequalities
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society