Some inequality relations involving multivalent functions

Let f(z) be a multivalent function, i.e., analytic on the unit disk and of the form f(z)=z^p + a_p+1z^p+1 +...�, p=2,3,.... In this work we give su�fficient conditions (unfortunately not sharp) when the following implications hold:
�|arg �[1 +zf^(p+1)(z)/f^(p)(z)]|<�(alpha pi)/2 (z in D)
�implies
|arg zf^(p)(z)/f^(p-1)(z)|<(beta_1 pi)/2 (z in D)
and
|arg zf^(p)(z)/f^(p-1)(z)|<(beta_1 pi)�/2 (z in D)
�implies
|arg zf^(p-1)(z)/f^(p-2)(z)|<�(beta_2 pi)�/2 (z in D).