Bi-Univalent Functions of Complex Order Defined by Hohlov Operator Associated with $(\mathcal {P,Q})-$Lucas Polynomial

Abstract

On this study, two new subclasses of the function class $\Xi$ of bi-univalent functions of complex order defined in the open unit disc are introduced and investigated. These subclasses are connected to the Hohlov operator with $(\mathcal {P,Q})-$Lucas polynomial and meet subordinate criteria. For functions in these new subclasses, we also get estimates for the Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$. The results are also discussed as having a number of (old or new) repercussions.

Keywords

• analytic functions
• univalent functions
• bi-univalent functions
• bi-starlike and bi-convex functions
• hohlov operator
• gaussian hypergeometric function
• (p
• q)-lucas polynomial