Sentence examples for bounded sequence defined on from inspiring English sources

where { h ( n ) } is a bounded sequence defined on the set of nonnegative integers Z +.

H ( n ) is a nonnegative sequence defined on Z + such that ∑ n = 0 ∞ H ( n ) = 1 and x ( n ) is a nonnegative bounded sequence defined on Z with x ∗ ≤ lim inf n → ∞ x ( n ) ≤ lim sup n → ∞ x ( n ) ≤ x ∗, where x ∗, x ∗ are nonnegative constants.

Let be a positive sequence defined on, and let and be nonnegative sequences defined on.

Assume that have Browder's property and for every, where is a bounded sequence in defined by (2.10).

The space (ell^{infty}_{n_{0}}) is the set of real sequences defined on the set of positive integers where any individual sequence is bounded with respect to the usual supremum norm.

The space (l^{infty}_{n_{0}}) is the set of real sequences defined on the set of positive integers where any individual sequence is bounded with respect to the usual supremum norm.

Throughout this paper, assume that, and stand for the sets of all positive integers and integers, respectively,,,,, and denotes the set of real sequences defined on the set of positive integers lager than where any individual sequence is bounded with respect to the usual supremum norm for.

Let be nonnegative sequences defined on and for each.

We show that ((g_{k})) be a bounded sequence on ([0, n]).

Let ({x_{n}}) be a bounded sequence on a reflexive Banach space X.

,, and are nonnegative bounded sequences of real numbers defined on such that (2.2).