Sentence examples for be a sequence for from inspiring English sources

Proof Let { x n } ⊂ X be a sequence for which I r ( x n ) → c ∈ R and (4.8) holds true with ε n → 0. Since X is finite dimensional, it is sufficient to prove that { x n } is bounded.

Let be a sequence of scalars with for all.

Let be a sequence of nonexpansive self-mappings on such that and is a sequence in for some.

Let be a sequence of nonexpansive self-mappings on such that and let be a sequence in for some.

Let be a sequence of nonexpansive mappings of into itself such that, and let be a sequence in for some.

It is clear that is a sequence for martingale difference.

x is a sequence for which there is a convergent sequence y such that (x_{n}=y_{n}) for a.a.n.  .

x is a statistically convergent sequence; x is a statistically Cauchy sequence; x is a sequence for which there is a convergent sequence y such that (x_{n}=y_{n}) for a.a.n.

If x is a sequence for which there is an F̂-statistically convergent sequence y such that (widehat{F}x_{k}=widehat{F}y_{k}) for almost all k, then x is an F̂- statistically convergent sequence.

Let and be a sequence in for some.

where is the mapping defined by (2.4) and be a sequence in for all.