INEQUALITIES FOR THE NON-TANGENTIAL DERIVATIVE AT THE BOUNDARY FOR HOLOMORPHIC FUNCTION

Abstract

In this paper, we present some inequalities for the non-tangential derivative of f(z). For the function f(z) = z+b(p)+(1)z(P+1) +b(p)+(2)z(P)+2 + . . . defined in the unit disc, with R(f'(z)/lambda f'(z)+1-lambda) beta, 0 > beta, 0 <= beta < 1, 0 <= lambda < 1, we estimate a module of a second non-tangential derivative of f(z) function at the boundary point xi, by taking into account their first nonzero two Maclaurin coefficients. The sharpness of these estimates is also proved.