ON THE MUTUAL CHANGE OF VALUES OF THE DERIVATIVE AND THIRD COEFFICIENT IN A CLASS OF REGULAR FUNCTIONS

摘要

Let T be the class of functions f(z) = z + ∑~∞_(n=2) c_nz~n regular and typically real in the disk |z| < 1. Sharp estimates for the derivative f'(r) (0 < r < 1) in terms of the value C_3 and sharp estimates for the coefficient c_3 in terms of f'(r) are obtained. Bibliography: 6 titles.