The Set of Values of Functionals in the Classes of Functions Having Integral Representation

Abstract

This paper presents a certain method to determine the set of values of the functional (equation) defined on the family of analytic functions in the unit disc possessing an integral representation with kernel q(z,t) in the interval [α ,β ]. It has been shown that the set of values of the linear functional J[ f( z )] at the point z₀ is the convex hull of the curve Γ, given by (equation). The Class of Functions with Limited Rotation was cosidered as a special case and some new results were obtained.