International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 2, Pages 259-266
doi:10.1155/S0161171288000316

On a class of p-valent close-to-convex functions of order β and type α

Abstract

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