On coefficient theorems for starlike and quasi-convex of type B mappings in complex Banach spaces
Year: 2026
Type: preprint
Abstract: 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 $f(0) = 1$ and $X$ is a complex Banach space with the unit ball $\mathbb{B}$. The main contributions of this paper are threefold. First, we establish a sufficient coefficient condition for a function $F(z)=zf(z)$ to be starlike and quasi-convex of type $B$ in a complex Banach space. Second, we prove that the Bieberbach conjecture holds for these classes of functions. Finally, we analyze the difference of coefficients for such functions in this setting. The results established here directly extend the previous results to the broader setting of complex Banach spaces.
Source: arXiv (Cornell University)
Authors: Sokol, Janusz, Majumder, Sujoy, Haldar, Goutam
Institution: Raiganj University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222681258