On Subclasses Of Bi-Starlike Functions Defined By Tremblay Fractional Derivative Operator

Abstract

In this paper, we introduce and investigate new subclasses of strongly bi-starlike and bi-starlike functions defined by Tremblay fractional derivative operator in the open unit disk. Also we obtain upper bounds for the coefficients $|a_{2}|$ and $|a_{3}|$ of functions belonging to these classes. Unlike recent studies, we use different technique for obtain the upper bounds on the coefficients $|a_{3}|$. Theorems proved in this paper generalizes the results given in [3].