Sentence examples for a sequence of weakly from inspiring English sources

Let E be a Banach space, and let C 1, C 2, C 3, … be a sequence of weakly closed subsets of E.

Thus ({T_{n}}_{ninBbb{N}}) is a sequence of weakly relatively nonexpansive mappings which is not a sequence of relatively nonexpansive mappings.

Let ({mathcal{A}_{k}}) be a sequence of nonnegative, weakly symmetric tensors of order m and dimension n, and (mathcal{A}_{k} - mathcal{A}_{k+1}) be nonnegative for each positive integer k.

If is a sequence of such that weakly and, then is a fixed point of.

To show (2.16), we choose a sequence of that converges weakly to such that (2.17).

Let ({X_{n}, ngeq1}) be a sequence of random variables weakly upper bounded by a random variable X.

Let ({ Z_{n},ngeq1}) be a sequence of random variables weakly dominated by a random variable Z, that is, (n^{-1}sum_{i=1}^{n}mathbb {P}(|Z_{i}|>x leq Cmathbb{P}(|Z|>x)) for any (xgeq0).

To see this, let ((x_{n})) be a sequence of M that converges weakly to some (xin M).

It is easy to see that if μ is a Banach limit and { x n } is a sequence of H which converges weakly to p ∈ H, then G ( { x k }, μ ) = p. We need the following lemma in the proof of Theorem 3.1.

To see this, take x ∗ ∈ w w ( x n ) and let { x n k } be a sequence of { x n } weakly converging to x ∗.

A sequence of distributions Λ i converges weakly to a distribution Λ if begin{array}{*{20}l} {lim}_{i to infty} Lambda_{i} phi) = Lambda phi end{array} (28).