Differential subordination and Bazilevič functions (Q1917749)

Let \(p\), \(\lambda\), \(h\) and \(\phi\) be analytic functions in the unit disc \(\Delta\). In this paper, the author proves that, under suitable assumptions on the above functions, the following relation holds: \(p(z)+ \lambda(z)zp'(z)\prec h(z)\) implies \(p(z)\prec \phi(z)\prec h(z)\) for \(z\in\Delta\), where \(\prec\) denotes the subordination of functions. Basing himself on this result he proves a sufficient condition for an analytic function to be starlike in \(\Delta\). These results are some extensions of the classical result of Sakaguchi and Libera.