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Radius of Ma-Minda Starlikeness and Convexity for Functions with Bounded Second Derivative

  • Poomalai Palanisamy
  • Ravichandran Vaithiyanathan
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Abstract

A normalized analytic function f(z)=z+∑k=n+1∞akzk defined on the unit disk 𝔻 is called Ma--Minda starlike or Ma--Minda convex if $zf'(z)/f(z)$ or 1+zf''(z)/f'(z), respectively, is subordinate to a Ma--Minda function φ. In this paper, we investigate the radii of Ma--Minda starlikeness and convexity for functions satisfying |f''(z)|<M in 𝔻. We first develop a unified approach for determining these radii and then apply it to obtain explicit radius estimates for several important choices of the Ma--Minda function~φ.

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Cite

BibTeXRIS
BibTeX
@misc{palanisamy2026radius,
  title = {{Radius of Ma-Minda Starlikeness and Convexity for Functions with Bounded Second Derivative}},
  author = {Poomalai Palanisamy and Ravichandran Vaithiyanathan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.07845},
  eprint = {2610.07845},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.07845},
}
RIS
TY  - UNPB
TI  - Radius of Ma-Minda Starlikeness and Convexity for Functions with Bounded Second Derivative
AU  - Poomalai Palanisamy
AU  - Ravichandran Vaithiyanathan
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.07845
UR  - https://arxiv.org/abs/2610.07845
AB  - A normalized analytic function f(z)=z+∑_k=n+1^∞a_kz^k defined on the unit disk 𝔻 is called Ma--Minda starlike or Ma--Minda convex if $zf'(z)/f(z)$ or 1+zf''(z)/f'(z), respectively, is subordinate to a Ma--Minda function φ. In this paper, we investigate the radii of Ma--Minda starlikeness and convexity for functions satisfying |f''(z)|<M in 𝔻. We first develop a unified approach for determining these radii and then apply it to obtain explicit radius estimates for several important choices of the Ma--Minda function~φ.
ER  -