Sentence examples for bounded then the sequence from inspiring English sources

If x0 ∈ E and the sequence is bounded, then the sequence is also bounded.

If { T y n } is bounded, then the sequence { x n } converges strongly to the unique fixed point of T.

Let x ∈ E. If { D f ( x, x n ) } is bounded, then the sequence { x n } is bounded too.

When the ( C ) c ∗ sequence is bounded, then the sequence is a ( PS ) c ∗ sequence (see [11]).

If the sequence ({D_{f} x,x_{n})}) is bounded, then the sequence ({x_{n}}) is also bounded.

When the ( C ) c ∗ sequence is bounded, then the sequence is a ( P S ) c ∗ sequence (see [11]).   3.

If is bounded, then the Ishikawa iteration sequence with errors converges to a fixed point of in.

Since sequence is bounded, then the subsequences and must converge.

Interestingly, given the fact that is bounded, then both sequences {x t } and {z t } are bounded.

Since d > 0, the sequence { | v n k | } is bounded, and then the sequence { v n k } is bounded in R N. By passing to a subsequence, we can assume that v n k → ξ as k → ∞, for some ξ ∈ R N. Then we obtain φ ( x, v n k ) → φ ( x, ξ ) as k → ∞ and the relation (3.2) implies that 0 = lim k → ∞ 〈 φ ( x, v n k ) − φ ( x, v ), v n k − v 〉 = 〈 φ ( x, ξ ) − φ ( x, v ), ξ − v 〉.

Let be a modulus function and the sequence be bounded; then (2.2). and the inclusions are strict.