Open AccessOn the rapidly convergence in capacity of the sequence of holomorphic functions
Author(s) -
Kieu Phuong
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1909627c
Subject(s) - mathematics , holomorphic function , sequence (biology) , bounded function , domain (mathematical analysis) , boundary (topology) , convergence (economics) , constant (computer programming) , combinatorics , discrete mathematics , pure mathematics , mathematical analysis , genetics , computer science , economics , biology , programming language , economic growth
In this paper, we are interested in finding sufficient conditions on a Borel set X lying either inside a bounded domain D ? Cn or in the boundary ?D so that if {rm}m?1 is a sequence of rational functions and {fm}m?1 is a sequence of bounded holomorphic functions on D with {fm-rm}m?1 is convergent fast enough to 0 in some sense on X then the convergence occurs on the whole domain D. The main result is strongly inspired by Theorem 3.6 in [3] whether the f fmg is a constant sequence.