A first-order differential double subordination with applications (Q427580)

Let \(q_1\) and \(q_2\) belong to a certain class of normalized analytic univalent functions in the open unit disk of the complex plane. Sufficient conditions are obtained for normalized analytic functions \(p\) to satisfy the double subordination chain \(q_1\prec p(z)\prec q_2(z)\). The differential sandwich-type result obtained is applied to normalized univalent functions and \(\Phi\)-like functions. (Let \(\Phi\) be an analytic function in a domain containing the open unit disk, \(\Phi(0)=0\) and \(\Phi^\prime(0)>0\). A function \(f\), analytic in the unit disk with \(f(0)=0\), \(f^\prime(0)=1\) is called \(\Phi\)-like if Re\(\frac{zf^\prime(z)}{\Phi(f(z))}>0\), \(z\) in the unit disk.)