A new subclass of starlike functions

Abstract

Motivated by the Ronning-starlike class [Proc Amer Math Soc {\bf118}, no. 1, 189-196, 1993], we introduce new class $\mathcal{S}^*_c$ includes of analytic and normalized functions $f$ which satisfy the inequality $$ {\rm Re}\left\{\frac{zf'(z)}{f(z)}\right\}\geq\left \frac{f(z)}{z}-1\right \quad( z 1/2$ in $ z