Abstract

Let Kn(D) be a class of analytic in domain D functions such that [F(z); z0,...,zn] for any z0,...,zn ∈ D. The domain D is called by maximal Kn-domain of the family T of functions which are analytic in D, if for any neighborhood ε(ψ) of any boundary point ψ of D there exists a function from T which does not belong to Kn(D \smile ε(ψ)). The maximal domain of univalence, i.e., maximal K1 domain was investigated by Bulgarian mathematician L. Chakalov. In this paper as maximal Kn-domains the angular domains are examined. Kn-domains for two special classes of rational functions are established.

Highlights

  • of the family T of functions which are analytic in D

  • of D there exists a function from T which does not belong to Kn(D ε(ψ

  • maximal K1 domain was investigated by Bulgarian mathematician L. Chakalov

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Summary

Introduction

Пусть Kn(D) – класс аналитических в D функций, для которых n-ая разделенная разность [F (z); z0, . Область D называется максимальной Kn-областью семейства T аналитических в области D функций, если при присоединении к области D какой-либо окрестности произвольной граничной точки найдется функция из T , уже не принадлежащая классу Kn в расширенной области. Где – простой замкнутый контур, расположенный в области D и охватывающий все точки z0, .

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