Coefficient bounds for certain families of bi-Bazilevič and bi-Ozaki-close-to-convex functions

Abstract

The aim of this work is to introduce two families, $ \mathcal{B}_{\Sigma}(\wp; \vartheta) $ and $ \mathcal{O}_{\Sigma}(\varkappa; \vartheta) $, of holomorphic and bi-univalent functions involving the Bazilevič functions and the Ozaki-close-to-convex functions, by using generalized telephone numbers. We determinate upper bounds on the Fekete-Szegö type inequalities and the initial Taylor-Maclaurin coefficients for functions in these families. We also highlight certain edge cases and implications for our findings.

Keywords

• bi-univalent function
• holormorphic function
• bazilevič function
• ozaki-close-to-convex functions
• upper bounds
• telephone numbers
• fekete-szegö problem