Sufficient conditions for univalence and starlikeness

Abstract

It is known that the condition $mathfrak {Re} left{zf'(z)/f(z)right}>0$, $|z|<1$ is a sufficient condition for $f$, $f(0)=f'(0)-1$ to be starlike in $|z|<1$. The purpose of this <br />work is to present some new sufficient conditions for univalence and starlikeness.