Goodman’s conjecture and the coefficients of univalent functions
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- by Abdallah Lyzzaik and David Styer PDF
- Proc. Amer. Math. Soc. 69 (1978), 111-114 Request permission
Abstract:
Goodman’s conjecture (for a bound on the modulus of the nth coefficient of a p-valent function as a linear combination of the moduli of the first p coefficients) is considered in the special case of functions which are polynomials of univalent functions. For such functions, it is shown that Goodman’s conjecture is equivalent to a set of coefficient conjectures for normalized univalent functions.References
- A. W. Goodman, On some determinants related to $p$-valent functions, Trans. Amer. Math. Soc. 63 (1948), 175–192. MR 23910, DOI 10.1090/S0002-9947-1948-0023910-X
- Serge Lang, Algebra, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965. MR 0197234 A. Lyzzaik, Multivalent linearly accessible functions and close-to-convex functions, thesis, University of Cincinnati, Cincinnati, Ohio, 1977.
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 69 (1978), 111-114
- MSC: Primary 30A34
- DOI: https://doi.org/10.1090/S0002-9939-1978-0460619-7
- MathSciNet review: 0460619