Application of Pythagorean means and Differential Subordination
For $0\leq\alpha\leq 1,$ let $H_{\alpha}(x,y)$ be the convex weighted harmonic mean of $x$ and $y.$ We establish differential subordination implications of the form \begin{equation*} H_{\alpha}(p(z),p(z)\Theta(z)+zp'(z)\Phi(z))\prec h(z)\Rightarrow p(z)\prec h(z), \end{equation*} where $\Phi,\;...
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| Main Authors: | , |
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| Format: | Journal Article |
| Language: | English |
| Published: |
22-03-2022
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| Subjects: | |
| Online Access: | Get full text |
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| Summary: | For $0\leq\alpha\leq 1,$ let $H_{\alpha}(x,y)$ be the convex weighted
harmonic mean of $x$ and $y.$ We establish differential subordination
implications of the form \begin{equation*}
H_{\alpha}(p(z),p(z)\Theta(z)+zp'(z)\Phi(z))\prec h(z)\Rightarrow p(z)\prec
h(z), \end{equation*} where $\Phi,\;\Theta$ are analytic functions and $h$ is a
univalent function satisfying some special properties. Further, we prove
differential subordination implications involving a combination of three
classical means. As an application, we generalize many existing results and
obtain sufficient conditions for starlikeness and univalence. |
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| DOI: | 10.48550/arxiv.2203.11596 |