Let f: (0,3] →→→R such that f(x) = 1². • Show that f(r) < 1. • Show that f has no fixed point on (0,3]. Hint: Assume there were f(c) = c and derive a contradiction. • Show that the function f(x) = 1 from [0, ∞) to [0, ∞) has a fixed point c. Hint: Set f(x) = x = and show the resulting equation has a solution in [0, 00) using the the IVP.
Let f: (0,3] →→→R such that f(x) = 1². • Show that f(r) < 1. • Show that f has no fixed point on (0,3]. Hint: Assume there were f(c) = c and derive a contradiction. • Show that the function f(x) = 1 from [0, ∞) to [0, ∞) has a fixed point c. Hint: Set f(x) = x = and show the resulting equation 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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10.1. #2 A,B,C. Thanks.
![2. Let f : (0, ] –→ R such that f(x) = r².
Show that f(x) < z.
Show that f has no fixed point on (0, 3]. Hint: Assume there were f(c) = c and derive
a contradiction.
Show that the function f(x) = from [0, ∞0) to [0, 0) has a fixed point c. Hint: Set
f(x) = x and show the resulting equation has a solution in [0, 00) using the the IVP.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbb66fa7-7c22-4982-a22f-aaed542f65b3%2F3de517f8-8550-47ee-a121-09383e2ea1f1%2Fh2n5xu_processed.png&w=3840&q=75)
Transcribed Image Text:2. Let f : (0, ] –→ R such that f(x) = r².
Show that f(x) < z.
Show that f has no fixed point on (0, 3]. Hint: Assume there were f(c) = c and derive
a contradiction.
Show that the function f(x) = from [0, ∞0) to [0, 0) has a fixed point c. Hint: Set
f(x) = x and show the resulting equation has a solution in [0, 00) using the the IVP.
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