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

The aim of this work is to introduce two families, ${\mathcal{B}}_{\mathrm{\Sigma }}(\mathrm{\wp };\vartheta )$ and ${\mathcal{O}}_{\mathrm{\Sigma }}(\varkappa ;\vartheta )$, 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.