Argument estimates of certain meromorphic functions (Q2706505)

Let a function \(f(z) = z^{-1}+\sum^\infty_{k=0} a_kz^k\) be analytic in the region \(0 < |z|< 1\), let \(n\) denote a fixed non-negative integer and let \(D^nf(z)=z^{-1}\left(\frac{z^{n+1}f(z)}{n!}\right)^{(n)}\).NEWLINENEWLINENEWLINEThe author exploits differential subordination techniques to obtain various results concerning the relation \(-\frac{z(D^{n+1}f(z))'}{D^nf(z)}\prec h(z)\) and also estimates for expressions \(\left|\text{arg}\left(\frac{z(D^{n+1}f(z))'}{D^{n+1}g(z)}\pm\gamma\right) \right|\), where \(\gamma\) is a fixed non-negative number and \(g(z)\) is a meromorphic starlike function.