On maximal Kn domains for certain families of rational functions
Articles
Jevgenij Kiriyatzkii
Vilnius Gediminas Technical University
Eduard Kiriyatzkii
Vilnius Gediminas Technical University
Published 2008-12-21
https://doi.org/10.15388/LMR.2008.10
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Keywords

analytic function
divided difference
angular domain

How to Cite

Kiriyatzkii J. and Kiriyatzkii E. (2008) “ On maximal Kn domains for certain families of rational functions”, Lietuvos matematikos rinkinys, 48(proc. LMS), pp. 60–65. doi: 10.15388/LMR.2008.10.

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.

 

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