Norm estimates for function starlike or convex of order α

Abstract

For holomorphic functions f with {\rm Re}\{zf'(z)/f(z)\}>\alpha and {\rm 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-t0-convex of exponential order (\alpha, \beta) will also be con- sidered.