Journal of the
Korean Mathematical Society JKMS

We give several sharp estimates for some initial coefficients problems for the so-called gamma starlike functions $f$, analytic and univalent in the unit disk $\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}$, and normalized so that $f(0)=0=f'(0)-1$, and satisfying $\real \Big[\Big(1+\frac{zf''(z)}{f'(z)}\Big)^{\gamma } \Big(\frac{zf'(z)}{f(z)}\Big)^{1-\gamma}\Big]>0$.

Keywords: univalent, starlike, convex, gamma-starlike, coefficients

MSC numbers: Primary 30C45, 30C50