THE MAXIMUM OF SOME FUNCTIONAL FOR HOLOMORPHIC AND UNIVALENT FUNCTIONS WITH REAL COEFFICIENTS

Abstract

In the paper the maximum of the functional a k 2a m 3(a 3-αa 2 2) in the class S R of functions f(z)=z+Σ {n=2} ∞,a nz n, a n=overline{a n}, holomorphic and univalent in the unit disc is obtained for α real and k, m positive integers.