A Class of Analytic Functions with Missing Coefficients

Let T-n(A, B, gamma, alpha) (-1 <= B < 1, B < A, 0 < gamma <= 1 and alpha > 0) denote the class of functions of the form f(z) = z + Sigma(8)(k=n+1) a(k)z(k) (n is an element of N = {1, 2, 3, ... }), which are analytic in the open unit disk U and satisfy the following subordination condition f'(z) + alpha zf ''(z) < (1(Az)/(1 + Bz))(gamma), for (z is an element of U; A <= 1;0 < gamma < 1), (1 + Az)/(1 + Bz), for ( z is an element of U; gamma = 1). We obtain sharp bounds on Ref'(z), Ref(z)/z, vertical bar f(z)vertical bar, and coefficient estimates for functions f(z) belonging to the class T-n(A, B, gamma, alpha). Conditions for univalency and starlikeness, convolution properties, and the radius of convexity are also considered.