If ƒ : [0, 1] → R is a contraction, then it has a unique fixed point. Select one: O a. False, here is a counter example: ƒ(x) = x − 1. O b. True, because any continuous function has a fixed point. c. True, by the contraction mapping theorem. O d. False, here is a counterexample: f(x) = ½ x + 1.
If ƒ : [0, 1] → R is a contraction, then it has a unique fixed point. Select one: O a. False, here is a counter example: ƒ(x) = x − 1. O b. True, because any continuous function has a fixed point. c. True, by the contraction mapping theorem. O d. False, here is a counterexample: f(x) = ½ x + 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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![If ƒ : [0, 1] → R is a contraction, then it has a unique fixed point.
Select one:
a. False, here is a counter example: ƒ(x) = x − 1.
O b.
True, because any continuous function has a fixed point.
c.
True, by the contraction mapping theorem.
O d.
False, here is a counterexample: f(x)
=
x + 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fe1fc35-672a-49fd-831b-9642c77888ed%2F31debb5a-158b-4af9-81d8-1804ca799042%2Fnr5ovfl_processed.png&w=3840&q=75)
Transcribed Image Text:If ƒ : [0, 1] → R is a contraction, then it has a unique fixed point.
Select one:
a. False, here is a counter example: ƒ(x) = x − 1.
O b.
True, because any continuous function has a fixed point.
c.
True, by the contraction mapping theorem.
O d.
False, here is a counterexample: f(x)
=
x + 1.
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