Sentence examples for the boundedness of the sequence from inspiring English sources

The boundedness of the sequence { x n } yields.

The boundedness of the sequence { x n } follows.

It remains to prove the boundedness of the sequence in.

Now, we show the boundedness of the sequence ({x_{n}}).

The boundedness of the sequence { x n } yields our result.

and this gives the boundedness of the sequence (5.11).

Notice the boundedness of the sequences { x n } and { W n x n }.

The next lemma will be a useful tool to obtain the boundedness of the sequences generated by the algorithms and also to obtain the convergence of the whole sequence to the solution.

By virtue of ξ n → 0 (as n → ∞ ) and the boundedness of the sequences { f ( x n ) } and { B x n }, we firstly observe that lim n → ∞ ∥ y n − x n ∥ = lim n → ∞ ξ n ∥ σ f ( x n ) − B x n ∥ = 0, and lim n → ∞ ∥ z n − U y n ∥ = lim n → ∞ ( 1 − δ ) ξ n δ ∥ σ f ( x n ) − B x n ∥ = 0. Next, we estimate ∥ z n + 1 − z n ∥.

To prove the boundedness of the generated sequence ({x^{k}}), we assume that the algorithm generates an infinite sequence for simple.

The condition ((g_{4})) is the key to prove the boundedness of the Cerami sequence.