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arXiv · 2403.17563

Higher order differential subordinations for certain starlike functions

Neha Verma·S. Sivaprasad Kumar
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Abstract

In this paper, we employ a novel second and third-order differential subordination technique to establish the sufficient conditions for functions to belong to the classes $\mathcal{S}^*_s$ and $\mathcal{S}^*_{\rho}$, where $\mathcal{S}^*_s$ is the set of all normalized analytic functions $f$ satisfying $ zf'(z)/f(z)\prec 1+\sin z$ and $\mathcal{S}^*_{\rho}$ is the set of all normalized analytic functions $f$ satisfying $ zf'(z)/f(z)\prec 1+\sinh^{-1} z$.

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Neha Verma, S. Sivaprasad Kumar. 2024-03-26. Higher order differential subordinations for certain starlike functions. https://arxiv.org/abs/2403.17563

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