The radius of starlikeness of certain analytic functions
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- by P. L. Bajpai and Prem Singh PDF
- Proc. Amer. Math. Soc. 44 (1974), 395-402 Request permission
Abstract:
Let $f(z) = \tfrac {1}{2}[zF(z)]’$, where $F(z)$ is starlike of order $\alpha ,0 \leqq \alpha < 1$ in $D = \{ z:|z| < 1\}$. The purpose of this paper is to find out the disc in which $f(z)$ is starlike of order $\beta ,0 \leqq \beta < 1$. Results are best possible.References
- R. J. Libera and A. E. Livingston, On the univalence of some classes of regular functions, Proc. Amer. Math. Soc. 30 (1971), 327–336. MR 288244, DOI 10.1090/S0002-9939-1971-0288244-5
- A. E. Livingston, On the radius of univalence of certain analytic functions, Proc. Amer. Math. Soc. 17 (1966), 352–357. MR 188423, DOI 10.1090/S0002-9939-1966-0188423-X
- M. S. Robertson, Variational methods for functions with positive real part, Trans. Amer. Math. Soc. 102 (1962), 82–93. MR 133454, DOI 10.1090/S0002-9947-1962-0133454-X
- K\B{o}ichi Sakaguchi, A variational method for functions with positive real part, J. Math. Soc. Japan 16 (1964), 287–297. MR 177111, DOI 10.2969/jmsj/01630287
- V. Singh and R. M. Goel, On radii of convexity and starlikeness of some classes of functions, J. Math. Soc. Japan 23 (1971), 323–339. MR 281903, DOI 10.2969/jmsj/02320323
- V. A. Zmorovič, On bounds of convexity for starlike functions of order $\alpha$ in the circle $| z| <1$ and in the circular region $0<| z| <1$, Mat. Sb. (N.S.) 68 (110) (1965), 518–526 (Russian). MR 0197712
- Zeev Nehari, Conformal mapping, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1952. MR 0045823
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 44 (1974), 395-402
- MSC: Primary 30A32
- DOI: https://doi.org/10.1090/S0002-9939-1974-0340578-4
- MathSciNet review: 0340578