On support points for some families of univalent functions |
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Authors: | Gae sun Chung |
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Affiliation: | 1. Department of Mathematics, Ewha Women’s University, 120-750, Seoul, Korea
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Abstract: | Given a closed subset of the familyS* (α) of functions starlike of order α, a continuous Fréchet differentiable functional,J, is constructed with this collection as the solution set to the extremal problem ReJ(f) overS* (α). The support points ofS* (α) is completely characterized and shown to coincide with the extreme points of its convex hulls. Given any finite collection of support points ofS* (α), a continuous linear functional,J, is constructed with this collection as the solution set to the extremal problem ReJ(f) overS* (α). |
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