The radius of $\alpha$-convexity for the class of starlike univalent functions, $\alpha$-real
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- by Petru T. Mocanu and Maxwell O. Reade PDF
- Proc. Amer. Math. Soc. 51 (1975), 395-400 Request permission
Abstract:
We use a result due to GutljanskiÄ to obtain the radius of $\alpha$-convexity for the class ${S^ \ast }$ of starlike univalent functions for real $\alpha$.References
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V. Ja. GutljanskiÄ, On the domains of variability for some functionals, Trudy Tomsk. Gos. Univ. Ser. Mat. Meh. 200 (1968), 71-87. (Russian)
- Sanford S. Miller, Petru T. Mocanu, and Maxwell O. Reade, BazileviÄ functions and generalized convexity, Rev. Roumaine Math. Pures Appl. 19 (1974), 213ā224. MR 338340
- Sanford S. Miller, Petru Mocanu, and Maxwell O. Reade, All $\alpha$-convex functions are univalent and starlike, Proc. Amer. Math. Soc. 37 (1973), 553ā554. MR 313490, DOI 10.1090/S0002-9939-1973-0313490-3 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.
Additional Information
- © Copyright 1975 American Mathematical Society
- 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