Coefficient estimates for some general subclasses of analytic and bi-univalent functions

Abstract

In the present investigation, we consider two new general subclasses \(\mathcal {H}_{\Sigma }(\tau , \mu , \lambda , \gamma ; \alpha )\) and \(\mathcal {H}_{\Sigma }(\tau , \mu , \lambda , \gamma ; \beta )\) of the class \(\Sigma \) consisting of analytic and bi-univalent functions in the open unit disk \(\mathbb {U}\). For functions belonging to the two classes introduced here, we find estimates on the Taylor–Maclaurin coeffcients \(|a_{2}|\) and \(|a_{3}|\). Several connections to some of the earlier known results are also pointed out.