Starlike Functions Associated with a Non-Convex Domain
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929617295638528 |
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| author | Kumar, S. Sivaprasad Giri, Surya |
| author_facet | Kumar, S. Sivaprasad Giri, Surya |
| contents | We introduce and study a class of starlike functions associated with the non-convex domain \[ \mathcal{S}^*_{nc} = \left\{ f \in \mathcal{A} : \frac{z f'(z)}{f(z)} \prec \frac{1+z}{\cos{z}} =: φ_{nc}(z), \;\; z \in \mathbb{D} \right\}. \] Key results include the growth and distortion theorems, initial coefficient bounds, and the sharp estimates for third-order Hankel and Hermitian-Toeplitz determinants. We also examine inclusion relations, radius problems for certain subclasses, and subordination results.
These findings enrich the theory of starlike functions associated with non-convex domains, offering new perspectives in geometric function theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04819 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Starlike Functions Associated with a Non-Convex Domain Kumar, S. Sivaprasad Giri, Surya Complex Variables We introduce and study a class of starlike functions associated with the non-convex domain \[ \mathcal{S}^*_{nc} = \left\{ f \in \mathcal{A} : \frac{z f'(z)}{f(z)} \prec \frac{1+z}{\cos{z}} =: φ_{nc}(z), \;\; z \in \mathbb{D} \right\}. \] Key results include the growth and distortion theorems, initial coefficient bounds, and the sharp estimates for third-order Hankel and Hermitian-Toeplitz determinants. We also examine inclusion relations, radius problems for certain subclasses, and subordination results. These findings enrich the theory of starlike functions associated with non-convex domains, offering new perspectives in geometric function theory. |
| title | Starlike Functions Associated with a Non-Convex Domain |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2412.04819 |