Bi-univalent functions of complex order defined by Hohlov operator associated with legendrae polynomial

Abstract

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

Keywords

• analytic functions
• univalent functions
• bi-univalent functions
• bi-starlike and bi-convex functions
• hohlov operator
• gaussian hypergeometric function
• dziok-srivastava operator
• legendrae polynomial