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 Bazilevič functions


Author: Ram Singh
Journal: Proc. Amer. Math. Soc. 38 (1973), 261-271
MSC: Primary 30A32
DOI: https://doi.org/10.1090/S0002-9939-1973-0311887-9
MathSciNet review: 0311887
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we study two subclasses of the class $ B$--the so-called class of Bazilevič functions. It is known that $ B$ is a subclass of $ S$, the class of univalent functions in $ E = \{ z \vert \vert z\vert < 1 \}$. Some well-known results pertaining to various subclasses of $ S$ will follow as corollaries to the theorems which are obtained here.


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

  • [1] I. E. Bazilevič, On a case of integrability in quadratures of the Loewner-Kufarev equation, Mat. Sb. 37 (79) (1955), 471-476. (Russian) MR 17, 356. MR 0072949 (17:356e)
  • [2] S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969), 429-446. MR 38 #1243. MR 0232920 (38:1243)
  • [3] -, The radius of univalence of certain analytic functions, Proc. Amer. Math. Soc. 24 (1970), 312-318. MR 40 #4433. MR 0251202 (40:4433)
  • [4] 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 0232926 (38:1249)
  • [5] F. R. Keogh and S. S. Miller, On the coefficients of Bazilevič functions, Proc. Amer. Math. Soc. 30 (1971), 492-496. MR 0283191 (44:424)
  • [6] Y. Komatu, On starlike and convex mappings of a circle, Kōdai Math. Sem. Rep. 13 (1961), 123-126. MR 24 #A1376. MR 0131526 (24:A1376)
  • [7] R. J. Libera, Some classes of regular univalent functions, Proc. Amer. Math. Soc. 16 (1965), 755-758. MR 31 #2389. MR 0178131 (31:2389)
  • [8] A. E. Livingston, On the radius of univalence of certain analytic functions, Proc. Amer. Math. Soc. 17 (1966), 352-357. MR 32 #5861. MR 0188423 (32:5861)
  • [9] E. P. Merkes and D. J. Wright, On the univalence of a certain integral, Proc. Amer. Math. Soc. 27 (1971), 97-100. MR 42 #4720. MR 0269825 (42:4720)
  • [10] S. S. Miller, On the Hardy class of a Bazilevič function and its derivative, Proc. Amer. Math. Soc. 30 (1971), 125-138. MR 0288246 (44:5444)
  • [11] Z. Nehari and E. Netanyahu, On the coefficients of meromorphic schlicht functions, Proc. Amer. Math. Soc. 8 (1957), 15-23. MR 18, 648. MR 0083038 (18:648d)
  • [12] K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan 11 (1959), 72-75. MR 21 #5734. MR 0107005 (21:5734)
  • [13] D. K. Thomas, On Bazilevič functions, Trans. Amer. Math. Soc. 132 (1968), 353-361. MR 36 #5330. MR 0222278 (36:5330)
  • [14] J. Zomorski, On Bazilevič schlicht functions, Ann. Polon. Math. 12 (1962), 83-90.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30A32

Retrieve articles in all journals with MSC: 30A32


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0311887-9
Keywords: Univalent, Bazilevič, close-to-convex functions
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society