Certain Subclasses of Bi-univalent Functions Associated with the Chebyshev Polynomials Based on Hohlov Operator

G. Murugusundaramoorthy$^1$, K.Vijaya$^2$ and H.\"{O}.G\"{u}ney$^3$

In this paper we introduce and investigate two new subclasses of the function class $\Sigma$ of bi-univalent functions in the open unit disk, which are associated with the Hohlov operator, and satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-MacLaurin coefficients $|a_2|$ and $|a_3|$ for functions in these new subclasses by using Chebyshev polynomials. Several new consequences of these results are also pointed out.

Tbilisi Mathematical Journal, Vol. 11(2) (2018), pp. 153166