'lf(pi,a,JL+vi;z)l;;?: 1, -n[ 1 + p ]/2,

EXAMPLE 2.41. In this example we apply Theorem 2.3e to obtain a best dominant of a differential subordination. We consider the class 'P[h, q],

where h(z) = 6(M - 1)z and q(z) = M z, with M > 1. For I c; I = 1 and m ;;=: 1, the function ljf(r, s, t; z) = 2r + 4s + t - 6z satisfies

for Re [ t/<;] ;:::>: Mm(m-1). Hence the admissibility condition (2.3-1) is satisfied and 'I' E 'P[h, q] . Since the function q satisfies the differential

equation 'lf( q(z), zq'(z), z2q"(z); z) = h(z), by Theorem 2.3e we have: