All $\alpha$-convex functions are univalent and starlike
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- by Sanford S. Miller, Petru Mocanu and Maxwell O. Reade PDF
- Proc. Amer. Math. Soc. 37 (1973), 553-554 Request permission
Abstract:
The authors show that $\alpha$-convex functions are starlike, $- \infty \leqq \alpha \leqq \infty$, thus extending some earlier results.References
- Petru T. Mocanu, Une propriété de convexité généralisée dans la théorie de la représentation conforme, Mathematica (Cluj) 11(34) (1969), 127–133 (French). MR 273000
- Petru T. Mocanu and Maxwell O. Reade, On generalized convexity in conformal mappings, Rev. Roumaine Math. Pures Appl. 16 (1971), 1541–1544. MR 308381 —, The order of starlikeness of certain univalent functions, Notices Amer. Math. Soc. 18 (1971), 815. Abstract #71T-B182.
- Sanford S. Miller, Distortions properties of alpha-starlike functions, Proc. Amer. Math. Soc. 38 (1973), 311–318. MR 310222, DOI 10.1090/S0002-9939-1973-0310222-X
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 37 (1973), 553-554
- MSC: Primary 30A32
- DOI: https://doi.org/10.1090/S0002-9939-1973-0313490-3
- MathSciNet review: 0313490