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Linear spaces and linear-invariant families of locally univalent analytic functions

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Abstract

Let X be the set of functions f analytic in the unit disk D with derivatives f′(z)≠0 in D, that satisfy the growth restriction f″(z)/f′(z)=0((1−|z|)−1 (z∈D). The set X is equipped with a normed linear space structure. The topological structure of X and its relationship with linear-invariant families of locally univalent functions is investigated.

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Authors and Affiliations

  1. Department of Mathematics, The University of North Carolina, 27514, Chapel Hill, N.C., USA

    Douglas M. Campbell, Joseph A. Cima & John A. Pfaltzgraff

Authors
  1. Douglas M. Campbell
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  2. Joseph A. Cima
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  3. John A. Pfaltzgraff
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Additional information

This research was supported by the U. S. Army Research Office-Durham, Grant DA-ARO-D-31-124-G1151.

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Campbell, D.M., Cima, J.A. & Pfaltzgraff, J.A. Linear spaces and linear-invariant families of locally univalent analytic functions. Manuscripta Math 4, 1–30 (1971). https://doi.org/10.1007/BF01168902

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  • DOI: https://doi.org/10.1007/BF01168902

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