Let S s ( α ) ( 0 ≤ α < 1 / 2 ) be the class of functions f ( z ) = z + ⋯ which are analytic in the unit disk and satisfy there \alpha$"> Re { z f ′ ( 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 S 0 ( α ) and T 0 ( α ) of S s ( α ) . We derive sharp distortion inequalities and some properties of the partial sums for functions in the classes S 0 ( α ) and T 0 ( α ) .