Abstract
Two large classes of analytic functions are defined, so that one contains the other. Sharp coefficient bounds for quadratic polynomials falling in the gap between these two classes are given.
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References
Jahangiri M, A gap condition for the zeros of certain polynomials in Kaplan classesK(α,β), Mathematika 34 (1987) 53–63
Kaplan W, Close-to-convex schlicht functions,Michigan Math. J. 1 (1952) 169–185
Marden M, The geometry of the zeros of a polynomial in a complex variable,Am. Math. Soc. Math. Surveys No. 3 (second edition) (1966)
Ruscheweyh St, Convolutions in geometric function theory In:Seminaire de Mathematiques superieures De L’Universite De Montreal Les Press (1982)
Sheil-Small T B, The Hadamard product and linear transformations of classes of analytic functions,J. Analyse Math. 34 (1978) 204–239
Sheil-Small T B, Coefficients and integral means of some classes of analytic functions,Proc. Am. Math. Soc. 88 (1983) 275–282
Sheil-Small T B, Some remarks on Bazilevic functions,J. Anal. Math. 43 (1983/84) 1–11
Suffridge T J, Polynomials in function theory,Contemp. Math. 38 (1985) 31–42
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Jahangiri, M. On the gap between two classes of analytic functions. Proc. Indian Acad. Sci. (Math. Sci.) 99, 123–126 (1989). https://doi.org/10.1007/BF02837799
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DOI: https://doi.org/10.1007/BF02837799