Sentence examples for exists sequence from inspiring English sources

For given, there exists sequence such that and as in view of the closedness of.

On the other hand, it follows form (F-) there exists sequence e m → ∞ such that lim m → ∞ sup x ∈ R N, x = e m x - 2 α ∑ t = 0 T F ( t, x ) = - ∞. Hence, if we choose b m = T e m, we have lim m → ∞ inf u ∈ H b m φ ( u ) = + ∞.

A nonself mapping T : K → E is called asymptotically nonexpansive if there exists sequence { k n } ⊂ [ 1, ∞ ), k n → 1 ( n → ∞ ) such that ∥ T ( P T ) n − 1 x − T ( P T ) n − 1 y ∥ ≤ k n ∥ x − y ∥ for all  x, y ∈ K, n ≥ 1. (1.7).

Then there exists sequences and, with and, such that (3.12).

Since, there exist sequence and disjont subsets of such that (2.6)  .

(3 If, then there exist sequences, such that.

If, then there exist sequences and with such that for.

if there exist sequences and in such that for some.

There exist sequences in and in such that as.

For such that, there exists such that and there exist sequences in and in such that.

Then there exist sequences in such that, and the sequences are convergent,,,.