Currently displaying 1 – 8 of 8

Showing per page

Order by Relevance | Title | Year of publication

Some generalizations of Olivier's theorem

Alain Faisant;  Georges Grekos;  Ladislav Mišík — 2016

Mathematica Bohemica

Let ∑ n = 1 ∞ a n be a convergent series of positive real numbers. L. Olivier proved that if the sequence ( a n ) is non-increasing, then lim n → ∞ n a n = 0 . In the present paper: (a) We formulate and prove a necessary and sufficient condition for having lim n → ∞ n a n = 0 ; Olivier’s theorem is a consequence of our Theorem . (b) We prove properties analogous to Olivier’s property when the usual convergence is replaced by the ℐ -convergence, that is a convergence according to an ideal ℐ of subsets of ℕ . Again, Olivier’s theorem is a consequence of...

Page 1

Download Results (CSV)