For $0\leq��\leq 1,$ let $H_��(x,y)$ be the convex weighted harmonic mean of $x$ and $y.$ We establish differential subordination implications of the form \begin{equation*} H_��(p(z),p(z)��(z)+zp'(z)��(z))\prec h(z)\Rightarrow p(z)\prec h(z), \end{equation*} where $��,\;��$ 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.