A sequence (f n)n of functions f n: X → ℝ almost decreases (increases) to a function f: X → ℝ if it pointwise converges to f and for each point x ∈ X there is a positive integer n(x) such that f n+1(x) ≤ f n (x) (f n+1(x) ≥ f n(x)) for n ≥ n(x). In this article I investigate this convergence in some families of continuous functions.
@article{bwmeta1.element.doi-10_2478_s11533-011-0030-2,
author = {Zbigniew Grande},
title = {On the almost monotone convergence of sequences of continuous functions},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {772-777},
zbl = {1232.26003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0030-2}
}
Zbigniew Grande. On the almost monotone convergence of sequences of continuous functions. Open Mathematics, Tome 9 (2011) pp. 772-777. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0030-2/
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