Certain subclasses of analytic functions and bi-univalent functions defined on the unite disc

Abstract

In this paper, Motivated by $q$- calculus, we introduce and investigate new subclasses of the analytic and bi-univalent functions defined in the open unit disk $U$. Estimates on the first two Taylor-Maclaurin coefficients $$ and $\left \vert a_{3}\right \vert $ for the functions belong to these new classes are obtained. Certain special cases are also indicated.