Bounded Doubly Close-to-Convex Functions

Abstract

We consider a new class $\mathcal{C}\mathcal{C}(\alpha ,\beta )$ of bounded doubly close-to-convex functions. Coefficient bounds, distortion theorems, and radius of convexity for the class $\mathcal{C}\mathcal{C}(\alpha ,\beta )$ are investigated. A corresponding class of doubly close-to-starlike functions ${\mathcal{S}}^{\mathrm{*}}\mathcal{S}(\alpha ,\beta )$ is also considered.