Alpha-convex functions in complex Banach spaces

Janusz Sokol, Sujoy Majumder, Goutam Halder

Let $\mathbb{B}$ be the unit ball in a complex Banach space $\mathbb{X}$. We study biholomorphic mappings $F:\mathbb{B}\to \mathbb{X}$ of the form $F(z)=f(z)z$ for $z \in \ma…