Show that the function f(z) = from [0, 0) to [0, ∞) has a fixed point c. Hint: Set f(r) = z and show the resulting eguation has a solution in (0. 00) using the the IVP.
Show that the function f(z) = from [0, 0) to [0, ∞) has a fixed point c. Hint: Set f(r) = z and show the resulting eguation has a solution in (0. 00) using the the IVP.
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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10.2.C. (3rd bullit point). Thanks.
![2. Let f : (0, ] → R such that f(x) = z².
• Show that f(x) < x.
• Show that f has no fixed point on (0, 1. Hint: Assume there were f(c) = c and derive
a contradiction.
• Show that the function f(x) = from [0, 0) to [0, ∞) has a fixed point c. Hint: Set
f(x) = z and show the resulting equation has a solution in [0. o0) using the the IVP.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbb66fa7-7c22-4982-a22f-aaed542f65b3%2F64d888cf-b57e-431c-919e-9c2da51e4525%2Fdwlpzzp_processed.png&w=3840&q=75)
Transcribed Image Text:2. Let f : (0, ] → R such that f(x) = z².
• Show that f(x) < x.
• Show that f has no fixed point on (0, 1. Hint: Assume there were f(c) = c and derive
a contradiction.
• Show that the function f(x) = from [0, 0) to [0, ∞) has a fixed point c. Hint: Set
f(x) = z and show the resulting equation has a solution in [0. o0) using the the IVP.
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