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 $$H_{\alpha}(p(z),p(z)\Theta(z)+zp'(z)\Phi(z))\prec h(z)\Rightarrow p(z)\prec h(z),$$ 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.
Citation
Shanmugam Sivaprasad Kumar. Priyanka Goel. "Application of Pythagorean means and Differential Subordination." Bull. Belg. Math. Soc. Simon Stevin 29 (3) 285 - 305, december 2022. https://doi.org/10.36045/j.bbms.210605
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