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 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 $h$ is a univalent function satisfying some special properties. Further, we prove involving combination three classical means. As an application, generalize many existing results obtain sufficient conditions for starlikeness univalence.