On a class of analytic functions with missing coefficients
Let T"n(A,B,@a) denote the class of functions of the form: f(z)=z+@?k=n+1~a"kz^k(n@?N={1,2,3,...}), which are analytic in the open unit disk U and satisfy the following subordination condition: f^'(z)+@azf^''(z)@?1+Az1+Bz(z@?U;-1=0). In this paper, we find the sharp lower bound on |z|=r<1 for the functional Re{f^'(z)+@azf^''(z)} over the class: T"n(A,B,0)=f(z)=z+@?k=n+1~a"kz^k:f^'(z)@?1+Az1+Bz(n@?N={1,2,3,...};z@?U). By applying this result, several interesting consequences are given.