Some applications of differential subordination for certain starlike functions

Abstract

We consider the class ${\mathcal{S}}^{\ast }(q_c)$ of normalized starlike functions $f$ analytic in the open unit disk $|z|<1$ that satisfying the inequality \begin{equation*} \left|\left(\frac{zf'(z)}{f(z)}\right)^2-1\right|<c \quad (0<c\leq1). \end{equation*} In this article, we present some subordination relations and these relations are then used to obtain some corollaries for some subclass of analytic functions.

7 pages, 2 figures

References in corpus (1)

• Univalence of the average of two analytic functions