Application of Pythagorean means and Differential Subordination

S. Sivaprasad Kumar; Priyanka Goel

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arXiv · 2203.11596

Application of Pythagorean means and Differential Subordination

S. Sivaprasad Kumar·Priyanka Goel

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Abstract

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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S. Sivaprasad Kumar, Priyanka Goel. 2022-03-22. Application of Pythagorean means and Differential Subordination. https://arxiv.org/abs/2203.11596

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