Abstract
Abstract This paper considers the following problem: for what value r, r < 1 {r<1} a function that is univalent in the unit disk | z | < 1 {|z|<1} and convex in the disk | z | < r {|z|<r} becomes starlike in | z | < 1 {|z|<1} . The number r is called the radius of convexity sufficient for starlikeness in the class of univalent functions. Several related problems are also considered.
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