Open AccessOn maximal Kn domains for certain families of rational functions
Author(s) -
Jevgenij Kiriyatzkii,
E. G. Kiriyatzkii
Publication year - 2008
Publication title -
lietuvos matematikos rinkinys
Language(s) - English
Resource type - Journals
eISSN - 2335-898X
pISSN - 0132-2818
DOI - 10.15388/lmr.2008.10
Subject(s) - domain (mathematical analysis) , mathematics , analytic function , boundary (topology) , rational function , class (philosophy) , function (biology) , maximal function , pure mathematics , combinatorics , mathematical analysis , computer science , artificial intelligence , evolutionary biology , biology
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.