Exercise 3. 1) Let (X, d) be a metric space. Show that f X → R is Lipschitz with Lipsch constant L if and only if f(x) ≤ f(y) + Ld(x, y), for all x, y € X. antrie
Exercise 3. 1) Let (X, d) be a metric space. Show that f X → R is Lipschitz with Lipsch constant L if and only if f(x) ≤ f(y) + Ld(x, y), for all x, y € X. antrie
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3.1
![**Exercise 3.**
1) Let \((X, d)\) be a metric space. Show that \(f: X \to \mathbb{R}\) is Lipschitz with Lipschitz constant \(\leq L\) if and only if
\[
f(x) \leq f(y) + Ld(x, y), \text{ for all } x, y \in X.
\]
*Note: The document has some parts obscured, so context might be missing.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa68164dd-6bba-4aa5-92bc-4824a71db092%2Faca1391a-eadf-4fa9-9be1-4a4183e112ea%2F119s5xn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise 3.**
1) Let \((X, d)\) be a metric space. Show that \(f: X \to \mathbb{R}\) is Lipschitz with Lipschitz constant \(\leq L\) if and only if
\[
f(x) \leq f(y) + Ld(x, y), \text{ for all } x, y \in X.
\]
*Note: The document has some parts obscured, so context might be missing.*
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