Estimates of conformal radius and distortion theorems for univalent functions

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A simple proof of the recent result by E. G. Emel’yanov concerning the maximum of the conformai radius r(D, 1) for a family of simply connected domains with a fixed value r(D, 0) is given. A similar problem is solved for a family of convex domains. Exact estimates for functionals of the form |g′ (w)|/|g(w)|δ are obtained for families of functions inverse to elements of the classes S and Sm, where S = (f: f is regular and univalent in the disk (z: |z| < 1) and f(0) f′(0) - 1 = 0) and S M = (f ∈ S: |f(z)| < M for |z| < 1).

Original languageEnglish (US)
Pages (from-to)3111-3120
Number of pages10
JournalJournal of Mathematical Sciences
Issue number6
StatePublished - 2002
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Applied Mathematics


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