Subordination by Univalent Functions

Sunder Singh, Ram Singh
1981 Proceedings of the American Mathematical Society  
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 univalent
more » ... on by univalent functions. A sufficient condition for a univalent function to be convex of order o is also given.
doi:10.2307/2044313 fatcat:nugwbwlsdfclthnbw4h3sy2q4u