On Differential Subordinations Related to Convex Functions

Let a gw0, 1x, p be an analytic function in the unit disk U with p 0.s0 and h belongs to the class S0c of convex functions with certain boundary normalization. In this paper the authors try to find the largest constant C a. for every a gw0, 1x such that the differential subordination of the form a zp9 z. p z. 1q $C a.h z., zgU p z. implies p$h in U. There is shown that 3r2.aFC a.F2a for every a gw0, 1x.