Abstract

Let S(A,B,p,α) denote the class of functions g(z)=zp+n=p+1bnzn analytic in the unit disc U={z:|z|<1} and satisfying the conditionzg(z)g(z)<p+[pB+(AB)(pα)]z1+Bz,zU,1B<A1,0α<p.Let C(A,B,p,β,α) denote the class of functions f(z)=zp+n=p+1anzn analytic in U, and satisfying the conditionRe{zf(z)g(z)}>β,zU,gS(A,B,p,α).In this paper we determine the coefficient estimates and distortion theorems for the class C(A,B,p,β,α).