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After the mapping, we obtained 1643 metabolites, to which there was at least one reaction associated with a gene measured in the dataset.
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Since every relatively nonexpansive mapping is a hemi-relatively nonexpansive mapping, we obtain the following result for a countable family of relatively nonexpansive mappings of modified Ishikawa iterative process.
And since is a nonexpansive mapping, we obtain (3.17).
Since T is a non-decreasing mapping, we obtain inductively (z_{n}leqbar{y}) for (ngeq0).
If S is an identity mapping, we obtain from Theorem 3.1 the following.
Since and is a nondecreasing mapping, we obtain by induction that (2.3).
Putting T n ≡ I the identity mapping, we obtain from Theorem 3.1 the following.
Noticing that and is a continuous mapping, we obtain that and.
For a single mapping, we obtain from Corollary 3.11 the following.
For a single mapping, we obtain from Theorem 3.8 the following.
In [8], putting g = i X (the identity mapping), we obtain the following result.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com