Subordination Method for the Estimation of Certain Subclass of Analytic Functions Defined by the q -Derivative Operator

Abstract

In this paper, we investigate an interesting class of analytic and biunivalent functions in the open unit disk $\Delta$ which is defined using the $q$ -derivative operator. We apply the subordination method to the functional of coefficients problem. Furthermore, we obtain the bounds of the certain functional of coefficients for functions in the class ${\mathcal{H}}_{\Sigma }^q\left(\lambda ,\beta \right)$ , for real and complex parameters. Also, an estimation for the initial Taylor and Maclaurin coefficients of functions in ${\mathcal{H}}_{\Sigma }^q\left(\lambda ,\alpha \right)$ was given.