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 considered.

Pre-Schwarzian and Schwarzian Derivatives of Harmonic Mappings

“…If ω is not constant, there exists a disk D(z 0 , R) ⊂ Ω where ω ′ = 0. Dividing (26) by ω ′ , we obtain…”

Norm estimates for convolution transforms of certain classes of analytic functions

“…Geometric and analytic properties of f relating the norm have been discussed in [10]. Many authors have given norm estimates for classical subclasses of univalent functions (see [4,8,11,14,15,24,25]). …”

Norm estimates for the Alexander transforms of convex functions of order alpha

“…The second inequality in part (i) was obtained in [7] while part (ii) was proved by S. Yamashita [18]. We remark that univalence of f does not necessarily imply that of J [f ] (see [3, p. 257]).…”

“…Many authors have given norm estimates for classical subclasses of univalent functions (see [2,6,9,14,17,18]). For a real number…”