A Subclass of bi-univalent functions by Tremblay differential operator satisfying subordinate conditions

Abstract

In this paper, we introduce a newly defined subclass $\mathcal{S}_{\Sigma}(\vartheta,\gamma,\eta;\varphi) $ of bi-univalent functions by using the Tremblay differential operator satisfying subordinate conditions in the unit disk. Moreover, we use the Faber polynomial expansion to derive bounds for the Fekete-Szego problem and first two \emph{Taylor-Maclaurin coefficients} $|a_2|$ and $|a_3|$ for functions of this class.

Keywords

• analytic function
• bi-univalent function
• coefficient estimates
• faber polynomial expansion
• tremblay fractional derivative operator