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Proof Let x = { x k } be a lacunary Δ-statistically convergent sequence which converges to L.
By the same process, we can construct a convergent sequence between m 1 and b, which converges to m 2 which is not less than b.
It follows that { u n } has a convergent subsequence, say again { u n }, which converges to u ∗.
which converges to as.
which converges to 2/3.
Then has a subsequence which converges to zero.
Let be a sequence of fixed points which converges to.
Let be a subsequence which converges to uniformly on.
Then { γ n } has a subsequence which converges to zero.
Let {x n } be a sequence in M which converges to some x ∈ X.
That is, there exists a Cauchy sequence { a i } i ∈ I ⊆ K which converges to a ˜.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com