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Metric space

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From Contraction Mapping.

The link to my textbook:
http://books.google.com/books?id=z8IaHgZ9PwQC&pg=PA72&dq=unique+solution+contraction+mapping&lr=#PPA66,M1

Section 8:Contraction Mapping from page 66 to page 77.
Please solve for #5 and #6 based on our reference.
If you have any question or suggestion, please contact me. Thank you.

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Solution Summary

This provides proofs of two statements regarding metric spaces.

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The explanations are in the file attached in two formats, pdf and Word 2007.

Problem 5:
Suppose condition (6) does not hold, so that there is some i=s for which
∑_j▒|a_sj | ≥1 (5.1)
Then, if we take, for instance, x'=(0,...,0) and x=(x_1,x_2,...x_n ) such that its components are
x_j={█(-1,if a_sj<0;@0, if a_sj=0;@1, if a_sj>0.)┤ ...

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