Definition
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[162] Let \(A⊂ ℝ\). A function \(f:A→ℝ \) is said Lipschitz continuous if there exists \(L{\gt}0\) such that \(∀ x,y∈ A\),
\[ |f(x)-f(y)|≤ L |x-y|~ ~ . \]
A function \(f:A→ℝ \) is said Hölder continuous if \(L{\gt}0\) and \(𝛼∈ (0,1]\) exist such that \(∀ x,y∈ A\),
\[ |f(x)-f(y)|≤ L |x-y|^𝛼~ ~ . \]