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).