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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On regions of $ \alpha $-convexity for starlike functions


Author: S. K. Bajpai
Journal: Proc. Amer. Math. Soc. 44 (1974), 365-368
MSC: Primary 30A32
MathSciNet review: 0344439
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Abstract: In this note an alternative proof to a result of Mocanu and Reade [see Notices Amer. Math. Soc. 20 (1973), A-107] on $ \alpha $-convexity region for starlike functions has been obtained.


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

  • [1] S. K. Bajpai and E. M. Silvia, On certain classes of analytic functions, Notices Amer. Math. Soc. 20 (1973), A-107. Abstract #701-30-17.
  • [2] Sanford S. Miller, Petru T. Mocanu, and Maxwell O. Reade, All 𝛼-convex functions are starlike, Rev. Roumaine Math. Pures Appl. 17 (1972), 1395–1397. Collection of articles dedicated to G. Călugăreanu on his seventieth birthday. MR 0324012 (48 #2364)
  • [3] P. T. Mocanu and M. O. Reade, The radius of $ \alpha $-convexity for the class of starlike univalent functions, $ \alpha $-real, Notices Amer. Math. Soc. 20 (1973). A-521. Abstract #706-30-3.
  • [4] Albert Schild, On starlike functions of order 𝛼, Amer. J. Math. 87 (1965), 65–70. MR 0174729 (30 #4929)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0344439-6
PII: S 0002-9939(1974)0344439-6
Keywords: Starlike, $ \alpha $-starlike, $ \alpha $-convex functions
Article copyright: © Copyright 1974 American Mathematical Society