The set of values of functionals in the classes of functions having integral representation

الملخص EN

This paper presents a certain method to determine the set of values of the functional J (f) = J a k(z) f{k /z) defined on the family of analytic functions in the unit disc possessing an integral representation with kernel q{z, t) in the interval [a, j8].

It has been shown that the set of values of the linear functional j [f (z j] at the point z0 is the convex hull of the curve T, given by equation Γ: w (t) = nΣ k=0 a k (z0) q (k), (z0, t) α ≤ t ≤ β.

The Class of Functions with Limited Rotation was considered as a special case and some new results were obtained.