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The radius of starlikeness of the convex combination tf(z) + (1 -t)g(z), 0 < / < 1, where f(z) and g(z) are normalized univalent starlike functions, is ru = Received by the editors August 21, 1978. AMS (MOS) subject classifications (1970). Primary 30A40, 30A32. Key words and phrases. Radius of starlikeness, closed convex hull of starlike univalent functions, Hadamard product. 'This author acknowledges the financial support of a University of Tasmania Research Studentship.doi:10.2307/2043039 fatcat:f3r7pt43t5hobkqqqyrznpuzwq