On close-to-convex functions

We consider a new subclass ${\tilde{\mathcal{K}}}_u$ of close-to-convex functions in the unit disk $\mathbb{D}:=\{z\in \mathbb{C}:\mathrm{\mid }z\mathrm{\mid }<1\}$. For this class, we obtain sharp estimates of the Fekete-Szegö problem, growth and distortion theorem, radius of convexity and estimate of the pre-Schwarzian norm.