Explain the concepts as well Let : RR be an increasing function. Suppose that there exist a, b ER satisfy ba and a ≤ f(a) and f(b) < b. Show that f has at least one fixed point., that is, there is some ER such that f(x)=x. (Hint: Consider suply ER: asusby≤ f(y)) and 2) can explain how to solve this?
Explain the concepts as well Let : RR be an increasing function. Suppose that there exist a, b ER satisfy ba and a ≤ f(a) and f(b) < b. Show that f has at least one fixed point., that is, there is some ER such that f(x)=x. (Hint: Consider suply ER: asusby≤ f(y)) and 2) can explain how to solve this?
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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![Explain the concepts as well
Let f: R→ R be an increasing function. Suppose that there exist a, b R satisfy
b>a and a ≤ f(a) and f(b) < b. Show that f has at least one fixed point., that is, there
is some z ER such that f(x) = x.
(Hint: Consider z:= sup{y ER: a ≤ y ≤ by ≤ f(y)} and 2)
can explain how to solve this?
why is fctn_a increase fcta?
why is the y values part of x values?
(f(b)<b
why is:
f(z)>z
why f(f(z)) what is it?
'et
and suppose
a foa)
NOW
N
and
From
and
then
AS
Since f
a ≤ f(a)
is increasing function
f(b)at.
we have
z = sup B
an increasing function.
fra) = f(b) →
_f(b) <b→ @
and
< f(a) = f(b) <b
B=yer: asy≤b, y ≤ fry] }
== sup &
if
f(=> >Z
f(f(x)) = f(z> >=
Fc=> EB.
Satisfy b> a and
falz -
from & D : f(z)=z
If zB: then t(=) == LO
consider ang xe đ
since
2 & 13 ond
⇒x<z
z = sup 12.
f(x) < fre)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa1ab2968-d288-4fd8-b87c-74963c459231%2F4c619349-86f6-43a2-95f8-3e31a4bcf25a%2Flfea4f9_processed.png&w=3840&q=75)
Transcribed Image Text:Explain the concepts as well
Let f: R→ R be an increasing function. Suppose that there exist a, b R satisfy
b>a and a ≤ f(a) and f(b) < b. Show that f has at least one fixed point., that is, there
is some z ER such that f(x) = x.
(Hint: Consider z:= sup{y ER: a ≤ y ≤ by ≤ f(y)} and 2)
can explain how to solve this?
why is fctn_a increase fcta?
why is the y values part of x values?
(f(b)<b
why is:
f(z)>z
why f(f(z)) what is it?
'et
and suppose
a foa)
NOW
N
and
From
and
then
AS
Since f
a ≤ f(a)
is increasing function
f(b)at.
we have
z = sup B
an increasing function.
fra) = f(b) →
_f(b) <b→ @
and
< f(a) = f(b) <b
B=yer: asy≤b, y ≤ fry] }
== sup &
if
f(=> >Z
f(f(x)) = f(z> >=
Fc=> EB.
Satisfy b> a and
falz -
from & D : f(z)=z
If zB: then t(=) == LO
consider ang xe đ
since
2 & 13 ond
⇒x<z
z = sup 12.
f(x) < fre)
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