On IA-density of points and some of its consequences

Autor:	Sayan Sengupta, Kumardipta Bose, Pratulananda Das
Rok vydání:	2017
Předmět:	Pure mathematics General Mathematics Mathematics
Zdroj:	Filomat. 31:6585-6595
ISSN:	2406-0933 0354-5180
Popis:	In this note, continuing in the line of [2] we further consider a more general approach and for y ? R and a sequence x = (xn) ? l? we define the more general notion of IA-density of indices of those xn?S which are close to y, denoted by I?A(y) where A is a non-negative regular matrix. Connections are drawn between I?A(y) and particular limit points of ((Ax)n). Our main result states that if x = (xn) is a bounded sequence, I?A(y) exists for every y ? R and ?y?D I?A(y) = 1 then I - limn??(Ax)n = ?y?D I?A(y)?y provided both finitely exists. This is an improvement of the alternative version of famous Osikiewicz Theorem given in [2].
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::78ec63fbec7f69114c999ec43436a8ef https://doi.org/10.2298/fil1720585d Zobrazit plný text záznamu