A generalized Fekete-Szegö functional and initial successive coefficients of univalent functions

The paper deals with sharp lower and upper estimations of the functional |c3(f)−λc2(f)2|−μ|c2(f)| in the class S, where λ∈C, μ∈R and cn(f) denotes the n-th coefficient of f. This functional can be regarded as a generalized Fekete-Szegö functional as it coincides with the classical one for μ:=0. The obtained results are applicable to estimate successive coefficients of holomorphic functions relative to univalent functions.