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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.19712 |
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| _version_ | 1866916183614160896 |
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| author | Kumar, S. Sivaprasad Verma, Neha |
| author_facet | Kumar, S. Sivaprasad Verma, Neha |
| contents | This article presents several findings regarding second and third-order differential subordination of the form: $$
p(z)+γ_1 zp'(z)+γ_2 z^2p''(z)\prec h(z)\implies p(z)\prec e^z $$ and $$
p(z)+γ_1 zp'(z)+γ_2 z^2p''(z)+γ_3 z^3p'''(z)\prec h(z)\implies p(z)\prec e^z. $$ Here, $γ_1$, $γ_2$, and $γ_3$ represent positive real numbers, and various selections of $h(z)$ are explored within the context of the class $\mathcal{S}^{*}_{e} := \{f \in \mathcal{A} : zf'(z)/f(z) \prec e^z\}$, which denotes the class of starlike functions associated with the exponential function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19712 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Second and Third order differential subordination for exponential function Kumar, S. Sivaprasad Verma, Neha Complex Variables This article presents several findings regarding second and third-order differential subordination of the form: $$ p(z)+γ_1 zp'(z)+γ_2 z^2p''(z)\prec h(z)\implies p(z)\prec e^z $$ and $$ p(z)+γ_1 zp'(z)+γ_2 z^2p''(z)+γ_3 z^3p'''(z)\prec h(z)\implies p(z)\prec e^z. $$ Here, $γ_1$, $γ_2$, and $γ_3$ represent positive real numbers, and various selections of $h(z)$ are explored within the context of the class $\mathcal{S}^{*}_{e} := \{f \in \mathcal{A} : zf'(z)/f(z) \prec e^z\}$, which denotes the class of starlike functions associated with the exponential function. |
| title | Second and Third order differential subordination for exponential function |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2403.19712 |