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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
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.
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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