Coefficient inequalities for certain classes of analytic functions of complex order

Abstract

Let $\Cal{Q}_{b}(\Phi ,\Psi ;\alpha )$ be the class ofnormalized analytic functions defined in the open unit disk andsatisfying$$\RE\left\{ 1+\frac{1}{b}\left( \frac{f(z)\ast \Phi(z)}{f(z)\ast \Psi (z)}-1\right) \right\} >\alpha$$for nonzero complex number $b$ and for $0\leq \alpha <1$.Sufficient condition, involving coefficient inequalities, for $f(z)$to be in the class $\Cal{Q}_{b}(\Phi ,\Psi ;\alpha )$ isobtained. Our main result contains some interesting corollaries asspecial cases.