2. Let [0, 1] := {ƒ : [0, 1] → R: f is a bounded function on [0, 1]}. Let ||f|| ∞ : sup f(x)| x[0,1] for fl[0, 1]. Show that ([0, 1], || ||) is a Banach space. =
2. Let [0, 1] := {ƒ : [0, 1] → R: f is a bounded function on [0, 1]}. Let ||f|| ∞ : sup f(x)| x[0,1] for fl[0, 1]. Show that ([0, 1], || ||) is a Banach space. =
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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![2. Let [0, 1] := {ƒ : [0,1] → R : f is a bounded function on [0, 1]}. Let
||f||
sup f(x)|
x= [0,1]
for fel [0, 1]. Show that ( [0, 1], || - ||) is a Banach space.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F655e5d67-ab19-404c-b883-3aa3c693f6a1%2Fdb29ca11-bbee-4252-8f8b-2a5bf8a1d555%2F8l644v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Let [0, 1] := {ƒ : [0,1] → R : f is a bounded function on [0, 1]}. Let
||f||
sup f(x)|
x= [0,1]
for fel [0, 1]. Show that ( [0, 1], || - ||) is a Banach space.
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