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This corollary satisfies all the conditions of Theorem 2.16 by taking (gx=I_{A}) (an identity mapping on A). □.
Let be a mapping on a set.
Let T be a mapping on a Hilbert space H.
Let be a mapping on a complete metric space.
Let be a mapping on a metric space such that (A) holds.
Let be a mapping on a metric space such that (B) holds.
Let T be an rth-order Lipschitz mapping on a complete metric space ((mathcal{X},d) ).
Let T be a mapping on a subset C of a Banach space X.
Let (T:Xrightarrowmathcal{K}(X)) be a mapping on a metric space ((X,d)).
The following lemma provides some useful properties of a firmly nonexpansive mapping on a Hilbert space.
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Let f : [ a, b ] → R be a L-Lipschitzian mapping on [ a, b ].
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com