Convolution Properties for Certain Subclass of Analytic Functions

Let S denote the class of analytic functions defined on Delta={z:vertical bar z vertical bar<1} which is normalized and has the Taylor series of the form f(z) = z+Sigma(infinity)(n=2)a(n)z(n). Let G(alpha,beta)(gamma,delta) be the subclass of S where the functions in this class satisfy the condition Ree(i delta){alpha f'(z)+beta zf ''(z)}>gamma for some alpha>0,beta >= 0 and 0 <=gamma<alpha cos delta with vertical bar delta vertical bar <=pi/2 and alpha cos delta-gamma>0. By making use of the theorem proved by Ruscheweyh and Sheil-Small, some convolution properties of the class G alpha,beta(gamma,delta) are obtained.