Faber polynomial coefficient bounds for \(m\)-fold symmetric analytic and bi-univalent functions involving \(q\)-calculus
Summary: In our present investigation, by applying \(q\)-calculus operator theory, we define some new subclasses of \(m\)-fold symmetric analytic and bi-univalent functions in the open unit disk \(\mathscr{U}=\{z \in \mathbb{C} : |z|<1\}\) and use the Faber polynomial expansion to find upper bounds of \(|a_{mk + 1}|\) and initial coefficient bounds for \(|a_{m + 1}|\) and \(|a_{2m + 1}|\) as well as Fekete-Szego inequalities for the functions belonging to newly defined subclasses. Also, we highlight some new and known corollaries of our main results.
scientific article; zbMATH DE number 7446733
scientific article