New subclasses of bi-univalent functions defined by multiplier transformation

Abstract

In the present paper, we introduce  new subclasses of the function class $\sum$ of bi-univalent functions by using multiplier transformation. Furthermore, we obtain estimates on the coefficients $|a_2|, |a_3|~\text{and}~|a_4|$ for functions of this class. Relevant connections of the results presented here with various well-known results are briefly indicated.