Sharp Robertson-type coefficient estimates for radial starlike and quasi-convex of type B mappings of order α in complex Banach spaces

In this paper, we study biholomorphic mappings $F:\mathbb{B}\to X$ of the form $F(z)=f(z)z$ for $z\in \mathbb{B}$, where $f:\mathbb{B}\to \mathbb{C}$ is a holomorphic function satisfying $f(0)=1$. Our main contributions are as follows: We establish sharp estimates for the coefficients of starlike functions of order $\alpha$ as well as quasi-convex functions of type $B$ and order $\alpha$ by employing the notion of majorization. The results established here directly extend the results due to Robertson \cite{Robertson-1936} to the broader setting of complex Banach spaces.