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)|
|Number of pages||10|
|Journal||Journal of Mathematical Sciences|
|State||Published - 2002|
ASJC Scopus subject areas
- Statistics and Probability
- Applied Mathematics