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Differential Subordinations and Harmonic Means

The aim of a study of the presented paper is the differential subordination involving harmonic means of the expressions \(p(z)\), \(p(z) + zp'(z)\), and \(p(z) + \frac{zp'(z)}{p(z)}\) when \(p\) is an analytic function in the unit disk, such that \(p(0)=1, p(z)\not \equiv 1\). Several applications in the geometric functions theory are given.