Norm estimates for function starlike or convex of order alpha (Q1288012)

For holomorphic functions \(f\) with \(\text{Re} \{zf'(z)/f(z)\} >\alpha\) and \(\text{Re} \{zf''(z)/f'(z)\} >\alpha-1\), \((0\leq \alpha<1)\), respectively, in \(\{| z| <1\}\), estimates of \(\sup_{| z| <1}(1-| z|^2) | f''(z)/f'(z) |\) are given. Functions Gelfer-close-to-convex of exponential order \((\alpha,\beta)\) will also be considered.