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

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).