Radii of Concavity for Subclasses of Univalent Functions Associated with the Exponential Mapping
Year: 2026
Type: preprint
Abstract: We determine the radii of concavity for the classes $\mathcal{S}_e^*$ and $\mathcal{C}_e$ of univalent functions associated with the exponential mapping $e^z$. Under the geometric framework of Avkhadiev--Wirths for conformal mappings with unbounded convex complements of opening angle $πA$ ($A \in (1,2]$), the radii are characterized by explicit transcendental equations. Sharpness is established globally by constructing explicit univalent extremal functions related to the disk automorphism $ω_0(z) = -z$, and the strict monotonicity of these radii with respect to the parameter $A$ is verified numerically.
Source: arXiv (Cornell University)
Authors: Das, Pradip, Sarkar, Nabadwip
Institutions: Raiganj University, Amity University Mumbai
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G489438624
OpenAlex ID: W7214078440