Estimates of Conformal Radius and Distortion Theorems for Univalent Functions |
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Authors: | L. V. Kovalev |
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Affiliation: | (1) The Institute of Applied Mathematics of the Far-Eastern Department of the Russian Academy of Sciences, Russia |
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Abstract: | A simple proof of the recent result by E. G. Emel'yanov concerning the maximum of the conformal 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 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 SM=for . Bibliography: 7 titles. |
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