  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.
