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Convex combination of analytic functions

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Abstract Radii of convexity, starlikeness, lemniscate starlikeness and close-to-convexity are determined for the convex combination of the identity map and a normalized convex function F given by f(z) = α… Click to show full abstract

Abstract Radii of convexity, starlikeness, lemniscate starlikeness and close-to-convexity are determined for the convex combination of the identity map and a normalized convex function F given by f(z) = α z+(1−α)F(z).

Keywords: convex combination; combination analytic; analytic functions; combination

Journal Title: Open Mathematics
Year Published: 2017

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