Some linear subordination results for classes of univalent functions
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- by Robert B. Byers PDF
- Proc. Amer. Math. Soc. 47 (1975), 143-146 Request permission
Abstract:
In this note we determine necessary and sufficient conditions on complex numbers $\lambda$ and $\mu$ such that $\lambda z/(1 - \mu {a_2}z)$ is subordinate to $f(z) = z + {a_2}{z^2} + \cdots$ for all functions $f$ in certain classes of univalent functions.References
- T. Başgöze, J. L. Frank, and F. R. Keogh, On convex univalent functions, Canadian J. Math. 22 (1970), 123–127. MR 257332, DOI 10.4153/CJM-1970-015-2
- S. D. Bernardi, Circular regions covered by schlicht functions, Duke Math. J. 32 (1965), 23–36. MR 171909
- W. K. Hayman, Multivalent functions, Cambridge Tracts in Mathematics and Mathematical Physics, No. 48, Cambridge University Press, Cambridge, 1958. MR 0108586
- F. R. Keogh, A strengthened form of the ${1\over 4}$ theorem for starlike univalent functions, Mathematical Essays Dedicated to A. J. Macintyre, Ohio Univ. Press, Athens, Ohio, 1970, pp. 201–211. MR 0274736
- Giovanni Sansone and Johan Gerretsen, Lectures on the theory of functions of a complex variable. II: Geometric theory, Wolters-Noordhoff Publishing, Groningen, 1969. MR 0259072
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 47 (1975), 143-146
- MSC: Primary 30A32
- DOI: https://doi.org/10.1090/S0002-9939-1975-0364619-4
- MathSciNet review: 0364619