QUESTIONS OF GEOMETRIC THEORY OF FUNCTIONS RELATED TO THE PRINCIPLE OF SUBORDINATION
The purpose of the article is to introduce a new class of univalent and analytic functions 𝐻(𝛼, 𝜇, 𝜆, 𝐴, 𝐵) and to investigate its geometric properties and isomorphism with other classes of functions. For the proof of theorems it is useful to generalize to the case of several complex variables the notion of chains of subordination Of H. Pommerenke [4]. This fact found its place in the first theorem of the article. In this paper we obtain necessary and sufficient conditions for estimating the coefficients of Taylor. Provided effectiveness ratings of Taylor in bicylinder and in the areas the boundaries of which are twice continuously differentiable and analytic convex externally. Given the bilateral evaluation module features a multiple circular restricted areas and installed accuracy to the special subsets. The radii of the star, convexity and close convexity of functions of the order 𝛾, 0 ≤ < 1 are constructed.