- #1

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## Homework Statement

Consider the system

x = [itex]\frac{1}{\sqrt{2}}[/itex] * [itex]\sqrt{1+(x+y)^2}[/itex] - 2/3

y = x = [itex]\frac{1}{\sqrt{2}}[/itex] * [itex]\sqrt{1+(x-y)^2}[/itex] - 2/3

Find a region D in the x,y-plane for which a fixed point iteration

x

_{n+1}= [itex]\frac{1}{\sqrt{2}}[/itex] * [itex]\sqrt{1+(x_n + y_n)^2}[/itex] - 2/3

y

_{n+1}= [itex]\frac{1}{\sqrt{2}}[/itex] * [itex]\sqrt{1+(x_n - y_n)^2}[/itex] - 2/3

is guaranteed to converge to a unique solution for any (x

_{0},y

_{0})[itex]\in[/itex]D

a) State clearly what properties this region must have

b) find a region with these properties and show it has these properties

## Homework Equations

Seen above

## The Attempt at a Solution

Not really sure where to start.

I don't know, in general, what properties are required.