Sentence examples for exists a weakly from inspiring English sources

Then, from the boundedness of ({u_{n_{j}}}), there exists a weakly convergent subsequence of ({u_{n_{j}}}).

By the weak compactness of C, there exists a weakly convergent subsequence { y n i } ⊆ { y n }.

Below we show that there exists a weakly relatively nonexpansive mapping which is not a relatively nonexpansive mapping.

Since is separable, the weak topology on is metrizable, and thus there exists a weakly convergent subsequence of, so that weakly, while as.

For every positive integer k there exists a weakly unimodal map (f:[0,1]to[0,1]) such that (i) (f(0)=f(1)=0),   (ii) f is (C^{k} -smooth,   (iii) f is not (C^{k} -smoothth.

Indeed, By reflexivity of E and boundedness of the sequence {x n } there exists a weakly convergent subsequence { x n j } ⊂ { x n } such that x n j ⇀ p for some p ∈ C. Now we show that p ∈ Fix ( S ).

Hence, a natural question arises: Q.1 Does there exist a weakly generalized recurrent manifold which is not any one of the following?

Let be a representation of a semigroup as norm nonexpansive and weakly continuous mappings from into and let be the enveloping semigroup of Let be a minimal left ideal of and let a minimal -invariant closed convex subset of Then there exists a nonempty weakly closed subset of such that is constant on.

We show that there exists a proper σ-weakly closed subalgebra of N⋊θR which contains N⋊θR+ and is not an analytic crossed product.

Since is bounded, so there exists a subsequence which converges weakly to.

As is bounded, there exists a subsequence which converges weakly to.