Weighted Harmonic Means

The purpose of this study is to develop a conception of the differential subordination involving harmonic means of the expressions \(\psi (p(z), zp'(z);z)\), where p is an analytic function in the unit disk, such that \(p(0)=1, p(z)\not \equiv 1\). Here, we discuss convex weighted harmonic means and we find some applications in the theory of analytic functions.