Let f be defined on an interval I. Suppose that there exists m > 0 anda> 0 such that: |f(x) – f(y)| < m|x – yla for all x, y E I (Such afunction is said to satisfy a Lipschitz condition of order a on I.a) Prove that f is uniformly continuous on I.

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Description: Let f be defined on an interval I. Suppose that there exists m > 0 anda> 0 such that: |f(x) – f(y)| < m|x – yla for all x, y E I (Such afunction is said to satisfy a Lipschitz condition of order a on I.a) Prove that f is uniformly continuous on I.

Let us assume "A" is a non empty subset of R, then f:E→R is uniformly continuous if and only if for…

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Let f be defined on an interval I. Suppose that there exists m > 0 and a> 0 such that: If (x) - f(y)| < m|x – ylª for all x, y E I (Such a function is said to satisfy a Lipschitz condition of order a on I. a) Prove that f is uniformly continuous on I.

Let f be defined on an interval I. Suppose that there exists m > 0 and a> 0 such that: If (x) - f(y)| < m|x – ylª for all x, y E I (Such a function is said to satisfy a Lipschitz condition of order a on I. a) Prove that f is uniformly continuous on I.

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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Let f be defined on an interval I. Suppose that there exists m > 0 and
a> 0 such that: |f(x) – f(y)| < m|x – yla for all x, y E I (Such a
function is said to satisfy a Lipschitz condition of order a on I.
a) Prove that f is uniformly continuous on I.

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