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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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.
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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