毕达哥拉斯方法的应用和不同的从属关系

Pub Date : 2022-03-22 DOI:10.36045/j.bbms.210605
S. S. Kumar, Priyanka Goel
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引用次数: 0

摘要

对于$0\leq\alpha\leq 1,$,设$H_{\alpha}(x,y)$为$x$和$y.$的凸加权调和平均值,我们建立了形式为\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*}的微分从属关系,其中$\Phi,\;\Theta$是解析函数,$h$是满足某些特殊性质的一价函数。进一步,我们证明了涉及三种经典方法组合的差异从属含义。作为应用,我们推广了许多已有的结果,得到了星似和同性的充分条件。
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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 $\Phi,\;\Theta$ 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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