- E9
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We work in the hypotheses of the theorem [1GD]. Show that, if \(f(⋅,y)\) is Lipschitz of constant \(L\) for every fixed \(y\), i.e.
\[ | f(x_ 1',y)- f(x_ 2',y)|≤ L |x_ 1'-x_ 2'|~ ~ ∀ x_ 1',x_ 2∈ U',y∈ J \](and \(L{\gt}0\) does not depend on \(x_ 1',x_ 2',y\)), then \(g\) is Lipschitz of constant \(L'\). What is the relationship between the constants \(L\) and \(L'\)?
Similarly if \(f\) is Hölderian.
Solution 1
EDB — 1GX
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English
Authors:
"Mennucci , Andrea C. G."
.
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