Abstract
Let S be the class of functions
, regular and univalent in the circle ¦Z¦ < 1. Assume that Dn (λ), n=2,3,..., are defined by the expansion
, ¦z¦<1,-1⩽λ⩽1. In the paper one obtains sharp estimates for D4(λ) in the class SR of functions from S with real coefficients C2,C3,... for all −1</λ⩽1. In particular, as a consequence, one obtains sharp estimates for the coefficients C3k+1 in the class SK/R of K-symmetric functions
from SR for all K=2,3,... For k=2, the last result strengthens a result of Leeman.
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Literature cited
G. B. Leeman, Jr.,“The seventh coefficient of odd symmetric univalent functions,” Duke Math. J.,43, No. 2, 301–307 (1976).
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 125, pp. 166–183, 1983.
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Fedorov, S.I. Estimates of the initial coefficients in the classes of univalent functions. J Math Sci 26, 2412–2423 (1984). https://doi.org/10.1007/BF01680023
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DOI: https://doi.org/10.1007/BF01680023