A function f: [a, b] → R is of bounded variation if and only if there is some V > 0 such for all a < xo S ¤1 S... Xn S b, EIf (Tk) – f(2k+1)| S V. k=1 Show that f can be written as difference of two monotone functions.
A function f: [a, b] → R is of bounded variation if and only if there is some V > 0 such for all a < xo S ¤1 S... Xn S b, EIf (Tk) – f(2k+1)| S V. k=1 Show that f can be written as difference of two monotone functions.
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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![A function f: (a, b] → R is of bounded variation if and only if there is some V > 0
such for all a < DO S ¤1 S... < In S b,
EIf (®k) – f(xk+1)| < V.
k=1
Show that f can be written as difference of two monotone functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F911ca249-35f6-404a-995c-99de90e03835%2Fa8a041d7-1db0-43cf-91a0-ff050b930a34%2Fjsiis87_processed.png&w=3840&q=75)
Transcribed Image Text:A function f: (a, b] → R is of bounded variation if and only if there is some V > 0
such for all a < DO S ¤1 S... < In S b,
EIf (®k) – f(xk+1)| < V.
k=1
Show that f can be written as difference of two monotone functions.
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