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On a subclass of Bazilevič functions


Authors: P. J. Eenigenburg, S. S. Miller, P. T. Mocanu and M. O. Reade
Journal: Proc. Amer. Math. Soc. 45 (1974), 88-92
MSC: Primary 30A32
DOI: https://doi.org/10.1090/S0002-9939-1974-0344441-4
MathSciNet review: 0344441
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Abstract: The authors show that certain Bazilevič functions are spiral-like. Then the authors study the growth and Hardy classes of those special functions.


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  • [1] T. Basgöze and F. R. Keogh, The Hardy class of a spiral-like function and its derivative, Proc. Amer. Math. Soc. 26(1970), 266-269. MR 41 #8680. MR 0264084 (41:8680)
  • [2] 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)
  • [3] P. L. Duren, Theory of $ {H^p}$ spaces, Pure and Appl. Math., vol. 38, Academic Press, New York, 1970. MR 42 #3552. MR 0268655 (42:3552)
  • [4] P. J. Eenigenburg and F. R. Keogh, The Hardy class of some univalent functions and their derivatives, Michigan Math. J. 17(1970), 335-346. MR 0306505 (46:5631)
  • [5] P. J. Eenigenburg and S. S. Miller, The $ {H^p}$ classes for $ \alpha $-convex functions, Proc. Amer. Math. Soc. 38(1973), 558-562. MR 0310216 (46:9318)
  • [6] S. S. Miller, Distortion properties of alpha-starlike functions, Proc. Amer. Math. Soc. 38(1973), 311-318. MR 0310222 (46:9324)
  • [7] S. S. Miller, P. Mocanu and M. O. Reade, All $ \alpha $-convex functions are univalent and starlike, Proc. Amer. Math. Soc. 37(1973), 553-554. MR 0313490 (47:2044)
  • [8] P. Mocanu, Une propriété de convexité généralisée dans la théorie de la repprésentation conforme, Mathematica (Cluj), 11(34)(1969), 127-133. MR 42 #7881. MR 0273000 (42:7881)
  • [9] P. Mocanu and M. O. Reade, On generalized convexity in conformal mappings, Rev. Roumaine Math. Pures Appl. 16(1971), 1541-1544. MR 0308381 (46:7495)
  • [10] C. Pommerenke, über die Subordination analytischer Funktionen, J. Reine Angew. Math. 218(1965), 159-173. MR 31 #4900. MR 0180669 (31:4900)
  • [11] T. Sheil-Small, On Bazilevič functions, Quart. J. Math. Oxford Ser. (2) 23(1972), 135-142. MR 45 #8847. MR 0299799 (45:8847)
  • [12] H. Yoshikawa, On a subclass of spiral-like functions, Mem. Fac. Sci. Kyushu Univ. Ser. A 25(1971), 271-279. MR 0310218 (46:9320)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0344441-4
Keywords: Bazilevič function, univalent, Hardy class, spiral-like, growth
Article copyright: © Copyright 1974 American Mathematical Society

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