Abstract
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].
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