On functions starlike with respect to symmetric and conjugate points

A class S-s*(alpha,beta) of functions f, regular and univalent in D = {z : \z\ < 1} given by f(z) = z + (n=2)Sigma(infinity) a(n)z(n) and satisfying the condition \zf'(z)/f(z) - f(-z) -1 \ < beta \ alpha zf'(z)/f(z) - f(-z) + 1\, z is an element of D, 0 less than or equal to alpha less than or equal to 1,0 < beta less than or equal to 1 is introduced and studied. An analogous class S-c* (alpha,beta) is also examined.