Compact metric space and contraction maps

Assignment Help Mathematics

Reference no: EM13132993

Here is the question.

Let (X,d) be a compact metric space, and let Con(X) denote the set of contraction maps on X. We shall define the distance between two maps f,g which belongs to Con(X) as follows :

d_c (f,g) = sup d ( f(x) , g(x) ) for any x that belongs to X.

a) Show that

d(y_f,y_g) <= d_c(f,g)/(1-min(cf,cg)) (where <= mean smaller or equal)

Where y_f and y_g are the fixed points of f and g, respectively, and cf and cg are their contraction factors.

b) What property regarding fixed points and contraction maps can be deduced from this result?

Reference no: EM13132993

Questions Cloud

Describe ethos-pathos and logos : Why is it important to follow a writing process when setting up an argument? What is your writing process like? What do you do to make sure you are reading critically? List your top three strategies and describe how they help your reading process.

Distance and bearing-army cadet : An army cadet is involved in a compass exercise. He leaves point O and walks 50m due west to point A. He then walks 80m due north to point B and finally 60m on a bearing of 320 deg to point C.

What are the main types of asset being amortized : Answer the following questions based on the 2011 annual report of Proctor & Gamble Corporation (P&G). A link to the annual report is provided below. The financial statements are on pp. 31-74 of the annual report, and all questions can be answered ..

What is the molar concentration of the ammonia : If 19.0 mL of 0.800 M HCl solution are needed to neutralize 5.00 rm mL of a household ammonia solution, what is the molar concentration of the ammonia?

Compact metric space and contraction maps : Let (X,d) be a compact metric space, and let Con(X) denote the set of contraction maps on X. We shall define the distance between two maps f,g which belongs to Con(X) as follows:

Using binomial pricing model estimate the fair value : The market price of the common stock was $31 per share at the date of the grant. G Corp. used the Binomial pricing model and estimated the fair value of each of the options at $10. What amount should G charge to compensation expense for the year e..

Types of symmetry : Describe objects that have each of the following types of symmetry.

Deep-colored magic : I agree with Connie, The Catalinas hold their own deep-colored magic,because when I was in the military is was station at white sands New Mexico, which east of Arizona, and six to eight hours away. While in the military I was in a program to help sin..

What is consolidated net income : During the current year, Jordan reported interest expense of $22,000 while Fey reported interest income of $21,000. What is consolidated net income?

User Account

All Pages