Some applications of differential subordination for certain starlike functions

Abstract

Let $\mathcal{S}^*(q_c)$ denote the class of functions $f$ analytic in the open unit disc $\Delta$, normalized by the condition $f(0)=0=f'(0)-1$ and satisfying the following inequality $\left|\left(\frac{zf'(z)}{f(z)}\right)^2-1\right|