Extension of Some Results of Inequality Relations Involving Multivalent Functions

In this paper, we extend our results of some inequality relations in which we include multivalent functions in order to give sufficient conditions (unfortunately not sharp) when the following implication holds: � � |arg[1 + zf^(p+1)(z)/f^(p)(z)]�| � � < απ/2 (z ∈ D) ⇒ � �|arg zf'(z)/f(z)| �< βπ/2 (z ∈ D). Here f(z) is a multivalent function, i.e., analytic on the unit disk and of the form f(z) = z^p + a_{p+1}z^p+1 + · · · ,p = 2,3...