International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 30, Pages 1923-1931
doi:10.1155/S0161171203205330

On Sakaguchi functions

Ding-Gong Yang1 and Jin-Lin Liu2

1Department of Mathematics, Suzhou University, Suzhou 215006, Jiangsu, China
2Department of Mathematics, Yangzhou University, Yangzhou 225002, Jiangsu, China

Received 20 May 2002

Copyright © 2003 Ding-Gong Yang and Jin-Lin Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let Ss(α)(0≤α<1/2) be the class of functions f(z)=z+⋯ which are analytic in the unit disk and satisfy there Re{zf′(z)/(f(z)−f(−z))}>α. In the present paper, we find the sharp lower bound on Re{(f(z)−f(−z))/z} and investigate two subclasses S0(α) and T0(α) of Ss(α). We derive sharp distortion inequalities and some properties of the partial sums for functions in the classes S0(α) and T0(α).