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A general approach to the Fekete-Szegö problem. (English) Zbl 1132.30007

The study offers a new method to solve the Fekete-Szegő problem for classes of close-to-convex functions defined in terms of subordination. The essence of this problem is concerned with inequalities for the coefficient functional

Λ μ (f)=a 3 -μa 2 2 =1 6f ''' (0) - 3μ 2 [f '' (0)] 2

which corresponds to subclasses of normalized univalent functions in the unit disk, that is f(z)=z+a 2 z 2 +a 3 z 3 ++μ[0,1]. The obtained results are applied to the class of strongly close-to-convex functions.

MSC:
30C45Special classes of univalent and multivalent functions
30C50Coefficient problems for univalent and multivalent functions