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 – y|ª for allx, y € I (Such a function is said to satisfy a Lipschitz condition of order a on I. d) Prove that if g is differentiable on an interval I, and if g' is bounded on I, then g satisfies a Lipschitz condition of order 1 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 – y|ª for allx, y € I (Such a function is said to satisfy a Lipschitz condition of order a on I. d) Prove that if g is differentiable on an interval I, and if g' is bounded on I, then g satisfies a Lipschitz condition of order 1 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.d) Prove that if g is differentiable on an inte

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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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.
d) Prove that if g is differentiable on an interval I, and if g' is bounded
on I, then g satisfies a Lipschitz condition of order 1 on I.

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