  Let A_n be the class of functions f(z) which are analytic in the open unit
disk U} with f(0)=0, f'(0)=1, f"(0)=f"'(0)=...=f^{(n)}=0 and f^{(n+1)}\neq0.
Applying the results due to S. S. Miller (J. Math. Anal. Appl. 65(1978),
289-305), some interesting starlikeness problems concerned with subordinations
are discussed. The results in the paper are extensions of results by M.
Obradovi\'c (Hokkaido Math. J. 27(1998), 329-335).
