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Estimates for inverse coefficients of univalent functions from integral means

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Abstract

The purpose of this note is to point out that sharp coefficient bounds for the inverses of univalent functions from certain families are fairly direct corollaries of results on integral means. As an example, in §1 the method is applied to the familiar schlicht classS. The resulting coefficient estimates for the inverses of functions inS were first obtained by K. Löwner. Following this prototype, in §2 we obtain corresponding results, which are new, for a classS(p) of meromorphic schlicht functions in |z|<1.

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Authors and Affiliations

  1. Washington University, 63130, St. Louis, Missouri, USA

    Albert Baernstein & Glenn Schober

  2. Indiana University, 47401, Bloomington, Indiana, USA

    Albert Baernstein & Glenn Schober

Authors
  1. Albert Baernstein
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  2. Glenn Schober
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This work was supported in part by grants from the National Science Foundation.

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Baernstein, A., Schober, G. Estimates for inverse coefficients of univalent functions from integral means. Israel J. Math. 36, 75–82 (1980). https://doi.org/10.1007/BF02761231

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  • DOI: https://doi.org/10.1007/BF02761231

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