Question: Prove that the K-K-M theorem is equivalent to Brouwer's theorem, that is, K-K-M theorem Brouwer's theorem The classic application of the Brouwer theorem in

Prove that the K-K-M theorem is equivalent to Brouwer's theorem, that is,
K-K-M theorem ⇔ Brouwer's theorem
The classic application of the Brouwer theorem in economics is to prove the existence of competitive equilibrium. We extract the mathematical essence in the following corollary, and then show how it applies to competitive equilibrium in example 2.95.

Step by Step Solution

★★★★★

3.36 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Let be a continuous operator on an dimensional simplex with vertices x 0 x 1 x For 0 1 let x where 0 ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

914-M-N-A-O (341).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

Prove Theorem. Ea??. E(SSA) = (k - 1)o? n i=1

Prove that the no-retraction theorem is equivalent to Brouwer's theorem. The following proposition, due to Knaster, Kuratowki, and Mazurkiewicz (K-K-M), is equivalent to the Brouwer theorem. It is...

To show that each of the hypotheses of Brouwer's theorem is necessary, find examples of functions f : S S with S R that do not have fixed points, where 1. f is continuous and S is convex but not...

1) Find all real solutions of: 4 2 2 x + x =3 2 x 4 + x23=0 4 2 2 2 x 2 x +3 x 3=0 x ( 21)=0 2 x 2 ( x 21)+ 3 ( 2 x2 +3 ) ( x 21 ) =0 ( 2 x2 +3 ) =0 2 2 x =3 3 x 2= 2 3 x= 2 3 x= i 2 2) Given the...

Applied Mathematics and Computation 95 (1998) 181192 Love dynamics: The case of linear couples Sergio Rinaldi 1 Centro Teoria dei Sistemi, CNR, Politecnico di Milano, Via Ponzio 34/5, 20133 Milan,...

\fCOMPLEX VARIABLES AND APPLICATIONS Eighth Edition James Ward Brown Professor of Mathematics The University of Michigan-Dearborn Ruel V. Churchill Late Professor of Mathematics The University of...

TOPIC: Isosceles Triangle Isosceles Triangle Ref/Info from book (pls read) Explore The Isosceles Triangle Recall the parts of the isosceles triangle. O vertex angle leg -leg base angle base angle R...

Convex geometry 0.1 Dehn-Sommerville relations In this section we will talk about convex polytopes. One possible denition of a convex polytope uses the notion of a half-space: A closed half-space in...

CHOOSE THE CORRECT ANSWER. @ Pro-test Directions: Read and analyze the questions below. Write onlyr the letter of the eorreet answer. 1. which theorem states that the sum of the lengths of an}.F two...

What type of layout(s) would be appropriate for: a. A grocery store? b. Home construction? c. Electronics assembly? d. A university?

Suppose that 18% of the employees of a given corporation engage in physical exercise activities during the lunch hour. Moreover, assume that 57% of all employees are male, and 12% of all employees...

does behavioral finance asserts that emotional investing produces higher returns?

All the following are project baselines that are generally part of the project management plan EXCEPT a. Technical b. Scope c. Time d. Cost

Continuation of Exercise 4-88. (a) If 30 separate one-hour intervals are chosen, what is the probability that no interval contains more than three arrivals? (b) Determine the length of an interval of...

The time between calls to a corporate office is exponentially distributed with a mean of 10 minutes. (a) What is the probability that there are more than three calls in one-half hour? (b) What is the...

Continuation of Exercise 4-90. (a) What is the probability that there are no calls within a two-hour interval? (b) If four non-overlapping one-half hour intervals are selected, what is the...

Given a screen that has an input thats takes 2 numbers and it makes a call to an API when you hit enter that sums the two and returns the value and the UI displays the results underneath the input,...

This problem has a few parts, shown in the picture! Use the invNorm command to find zo : (3 pts each: 12 pts total) ROUND the z-values to 3 decimal places. (b) Zo.12 (a) Zo.082 (d) zo.92 (c) Zo.89Do...