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PreprintCC BY 4.0arXiv

Radii of Concavity for Subclasses of Univalent Functions Associated with the Exponential Mapping

  • Pradip Das
  • Nabadwip Sarkar
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Abstract

We determine the radii of concavity for the classes 𝒮e* and 𝒞e of univalent functions associated with the exponential mapping ez. Under the geometric framework of Avkhadiev--Wirths for conformal mappings with unbounded convex complements of opening angle πA (A ∈ (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 ω0(z) = −z, and the strict monotonicity of these radii with respect to the parameter A is verified numerically.

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Cite

BibTeXRIS
BibTeX
@misc{das2026radii,
  title = {{Radii of Concavity for Subclasses of Univalent Functions Associated with the Exponential Mapping}},
  author = {Pradip Das and Nabadwip Sarkar},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26154},
  eprint = {2609.26154},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26154},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Radii of Concavity for Subclasses of Univalent Functions Associated with the Exponential Mapping
AU  - Pradip Das
AU  - Nabadwip Sarkar
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.26154
UR  - https://arxiv.org/abs/2609.26154
AB  - We determine the radii of concavity for the classes 𝒮_e^* and 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 ∈ (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.
ER  -