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Convex hulls of some classical families of univalent functions
1971
Transactions of the American Mathematical Society
Let S denote the functions that are analytic and univalent in the open unit disk and satisfy /(0) = 0 and/'(0) = 1. Also, let K, St, SR, and C be the subfamilies of 5 consisting of convex, starlike, real, and close-to-convex mappings, respectively. The closed convex hull of each of these four families is determined as well as the extreme points for each. Moreover, integral formulas are obtained for each hull in terms of the probability measures over suitable sets. The extreme points for each
doi:10.1090/s0002-9947-1971-0274734-2
fatcat:2y4tzs53hzecxj7oziyqzlv3m4