The 1-Dimensional Brouwer Fixed Point Theorem. It indicates that every continuous function mapping the closed interval
Question:
The 1-Dimensional Brouwer Fixed Point Theorem. It indicates that every continuous function ƒ mapping the closed interval [0, 1] to itself must have a fixed point; that is, a point c such that (c) = c.
Show that if ƒ is continuous and 0 ≤ ƒ (x) ≤ 1 for 0 ≤ x ≤ 1, then ƒ(c) = c for some c in [0, 1] (Figure 7).
Transcribed Image Text:
1 y с y = x y = f(x) X
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (5 reviews)
If f0 0 the proof is done with c 0 We may assume that f0 0 Let gx fx x g0 f0 0 f0 0 Since f...View the full answer
Answered By
Simon kingori
I am a tier-one market researcher and content developer who has been in this field for the last six years. I’ve run the freelancing gamut; from market research, data mining and SEO/SMM to copywriting, Content Development, you name it, I’ve done it. I’m extremely motivated, organized and disciplined – you have to be to work from home. My experience in Freelancing is invaluable- but what makes me a cut above the rest is my passion to deliver quality results to all my clients- it’s important to note, I've never had a dissatisfied client. Backed by a Masters degree in Computer Science from MOI university, I have the required skill set and burning passion and desire to deliver the best results for my clients. This is the reason why I am a cut above the rest. Having taken a Bsc. in computer science and statistics, I deal with all round fields in the IT category. It is a field i enjoy working in as it is dynamic and new things present themselves every day for research and exploration.
5.00+
1+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
The 1-Dimensional Brouwer Fixed Point Theorem. It indicates that every continuous function mapping the closed interval [0, 1] to itself must have a fixed point; that is, a point c such that (c) = c....
-
You have just been engaged as the auditor for Kasempa Company Ltd. During your first audit as the external auditor of the said company, you reviewed the accounting system and procedures operated by...
-
Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...
-
Starting with acetylene as your only source of carbon atoms, identify how you would prepare each member of the following homologous series of aldehydes: a. Ethanal b. Propanal c. Butanal d. Pentanal
-
Disher Cotton Farms is a large cotton producer located near Lubbock, Texas. Each year Disher plants its fields in cotton and then waits until the fall before the cotton is picked and sold. Disher...
-
What is the difference between shear stress and momentum flux? How are they related? Illustrate each one in terms of the angular flow in the gap in a cup and bob viscometer, in which the outer...
-
Owing to economical sample sizes and ease of application, probability-proportional to-size (PPS) sampling has become the most widely used statistical sampling plan in practice today, even by local...
-
Gulf Controls, Inc., has a net profit margin of 10 percent and earnings after taxes of $600,000. Its current balance sheet follows: a. Calculate Gulfs return on stockholders equity. b. The industry...
-
Elouise calculates the price/earnings ratio for the two companies listed below as follows: Will Corp Kunze Corp Price/Earnings Ratio 15.50 29.06 Based on these ratios, which company is expected to...
-
(a) Assume that g and h are continuous on [a, b]. Use Corollary 2 to show that if g(a) < h(a) and h(b) < g(b), then there exists c [a, b] such that g(c) = h(c). (b) Interpret the result of (a) in...
-
What is the sign of the coefficient multiplying x 7 if is a polynomial of degree 7 such that lim f(x) = o? X-00
-
What are the determinants of leading and lagging payments between related international affiliates?
-
Bizri Corporation had the following transactions during its first month of operations: Requirement Journalize the above transactions for Bizri Corporation. Purchases of raw materials on account...
-
Create a journal entry and a T-account entry for each of the following transactions: a. $30,000 worth of supplies purchased with cash b. $10,000 worth of supplies used to provide clients with goods...
-
Five errors have been found in the records of A V Kingfisher and require correction by general journal. a Courier charges paid through the petty cash book $55 ($50 + $5 GST) were posted in the...
-
In the accounts of A Bottlebrush, a tax invoice for the sale of stock $385 ($350 +$35 GST) to Glen Bawn was processed through the sales journal incorrectly as $836 ($760 + $76 GST). Control accounts...
-
Two machines were purchased in the financial year to 30 June 2022. Machine 1 is depreciated using the diminishing balance method at 35% p.a. It was purchased and installed on 31 January 2022 for $44...
-
Michaels Computers local bank offers the firm a 12-month revolving credit agreement of $500,000. The APR of the revolver is 12 percent with a commitment fee of 0.5% on the unused portion. Over the...
-
Show that the block upper triangular matrix A in Example 5 is invertible if and only if both A 11 and A 22 are invertible. Data from in Example 5 EXAMPLE 5 A matrix of the form A = [ A11 A12 0 A22 is...
-
Differentiate the function. (a) f(x) = 240 (b) f(t) = 2 - 2/3t (c) f(x) = x3 - 4x + 6 (d) g(x) = x2 (1 - 2x)
-
Differentiate the function. (a) f(x) = 240 (b) f(t) = 2 - 2/3t (c) f(x) = x3 - 4x + 6 (d) g(x) = x2 (1 - 2x)
-
Differentiate the function. (a) f(x) = 240 (b) f(t) = 2 - 2/3t (c) f(x) = x3 - 4x + 6 (d) g(x) = x2 (1 - 2x)
-
Watch the video and then respond to the questions that follow: ( How Babies See The World) (1) Explain how watching the video changes how you plan and prepare the learning environment and activities...
-
Consider the system: 3x + 2y + z = 2 x-y+3z = 9 2x+5y 11z = -46 Solve this system using a matrix inverse. (If a free variable is needed use the parameter t. If the system is inconsistent, enter...
-
What factors contribute to the emergence and success of social movements? Evaluate the role of resource mobilization, political opportunity structures, and framing in shaping the trajectory of...
Study smarter with the SolutionInn App