On $p$-close-to-star functions of order $\alpha$
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- by Hassoon S. Al-Amiri PDF
- Proc. Amer. Math. Soc. 29 (1971), 103-108 Request permission
Abstract:
In a recent paper M. Finkelstein has used an iterated form of Schwarzโs lemma to obtain growth estimates for convex functions and starlike functions of order zero. These estimates involve the second coefficient. W. E. Chase has announced results about the growth estimates and also about a radius of univalence and starlikeness for p-close-to-star functions of order zero. The author generalizes the above results to functions of order $\alpha$, $0 \leqq \alpha \leqq 1$.References
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Warren E. Chase, p-close-to-star-functions, Notices Amer. Math. Soc. 17 (1970), 172. Abstract #672-315.
- Mark Finkelstein, Growth estimates of convex functions, Proc. Amer. Math. Soc. 18 (1967), 412โ418. MR 214749, DOI 10.1090/S0002-9939-1967-0214749-8
- T. H. MacGregor, Functions whose derivative has a positive real part, Trans. Amer. Math. Soc. 104 (1962), 532โ537. MR 140674, DOI 10.1090/S0002-9947-1962-0140674-7
- Zeev Nehari, Conformal mapping, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1952. MR 0045823
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 103-108
- MSC: Primary 30.42
- DOI: https://doi.org/10.1090/S0002-9939-1971-0281894-1
- MathSciNet review: 0281894