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The radius of $ \alpha $-convexity for the class of starlike univalent functions, $ \alpha $-real


Authors: Petru T. Mocanu and Maxwell O. Reade
Journal: Proc. Amer. Math. Soc. 51 (1975), 395-400
MSC: Primary 30A32
DOI: https://doi.org/10.1090/S0002-9939-1975-0374404-5
MathSciNet review: 0374404
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Abstract: We use a result due to Gutljanskiĭ to obtain the radius of $ \alpha $-convexity for the class $ {S^ \ast }$ of starlike univalent functions for real $ \alpha $.


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

  • [1] V. Ja. Gutljanskiĭ, On the domains of variability for some functionals, Trudy Tomsk. Gos. Univ. Ser. Mat. Meh. 200 (1968), 71-87. (Russian)
  • [2] S. S. Miller, P. T. Mocanu and M. O. Reade, Bazilevič functions and generalized convexity, Rev. Roumaine Math. Pures Appl. 19 (1974), 213-224. MR 0338340 (49:3105)
  • [3] -, All $ \alpha $-convex functions are univalent and starlike, Proc. Amer. Math. Soc. 37 (1973), 553-554. MR 47 #2044. MR 0313490 (47:2044)
  • [4] P. T. Mocanu and M. O. Reade, The radius of $ \alpha $-convexity for the class of starlike functions, $ \alpha $-real, Notices Amer. Math. Soc. 20 (1973), A-112. Abstract #701-30-34.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0374404-5
Keywords: Starlike, convex, alpha-convex, univalent
Article copyright: © Copyright 1975 American Mathematical Society

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