On the Fekete-Szego problem for strongly $ \alpha $-quasiconvex functions

Abstract

The purpose of the present paper is to introduce the classes $ {\cal M}_\alpha(\beta)$ and $ {\cal P}_\alpha(\beta)$, respectively, of normalized strongly $ \alpha$-convex and $ \alpha$-quasiconvex functions of order $ \beta$ in the open unit disk and to obtain sharp Fekete-Szego inequalities for functions belonging to the classes $ {\cal M}_\alpha(\beta)$ and $ {\cal P}_\alpha(\beta)$.