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Let A' be the class of functions f(z) ~ z + a2z2 + • • • , which are regular and univalently convex in \z\ < 1. In this paper we establish certain subordination relations between an arbitrary member / of K, its partial sums and the functions (A/z)/£/(/)<* and y. f'Q t~lf(t)dt. The well-known result that z/2 is subordinate to f(z) in |z| < 1 for every/belonging to K follows as a particular case from our results. We also improve certain results of Robinson regarding subordination by univalentdoi:10.2307/2044313 fatcat:nugwbwlsdfclthnbw4h3sy2q4u