Coefficient inequalities for certain classes of analytic functions of complex order

B. A. Frasin

Let $\Cal{Q}_{b}(\Phi ,\Psi ;\alpha )$ be the class of normalized analytic functions defined in the open unit disk and satisfying $$ \REeft\{ 1+\frac{1}{b}eft( \frac{f(z)st \Phi (z)}{f(z)st \Psi (z)}-1\right) \right\} >lpha $$ for nonzero complex number $b$ and for $0\leq \alpha <1$. Sufficient condition, involving coefficient inequalities, for $f(z)$ to be in the class $\Cal{Q}_{b}(\Phi ,\Psi ;\alpha )$ is obtained. Our main result contains some interesting corollaries as special cases.