Let AC C([-1, 1]) be defined byA = {f € c'(I-1, 1), F(0) = 0, F'(x)| < 1, V xe (-1,1)}Prove that A is relatively compact in C([-1, 1]).

The set A is defined as A=f∈C1-1,1, f0=0, f'x≤1, ∀x∈-1,1. To prove that A is relatively compact.…

Answered: Let AC C([-1,1]) be defined by A =…

Let AC C([-1,1]) be defined by A = {f€c'(I-1, 1), f(0) = 0, f'(x)| < 1, V x€ (-1,1)} Prove that A is relatively compact in C([-1,1)).

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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Question

Let AC C([-1, 1]) be defined by
A = {f € c'(I-1, 1), F(0) = 0, F'(x)| < 1, V xe (-1,1)}
Prove that A is relatively compact in C([-1, 1]).

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