Abstract
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 language | English (US) |
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Pages (from-to) | 3111-3120 |
Number of pages | 10 |
Journal | Journal of Mathematical Sciences |
Volume | 110 |
Issue number | 6 |
DOIs | |
State | Published - 2002 |
Externally published | Yes |
ASJC Scopus subject areas
- Statistics and Probability
- General Mathematics
- Applied Mathematics