please friends can u help me with the question below

Q. If T is contraction, show that T^n (n\inN) is a contraction. If T^n is a contraction for all n>1, show that T need not be a contraction.

Thanks

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- May 26th 2011, 01:06 AMkinkongcontraction
please friends can u help me with the question below

Q. If T is contraction, show that T^n (n\inN) is a contraction. If T^n is a contraction for all n>1, show that T need not be a contraction.

Thanks - May 26th 2011, 01:31 AMgirdav
We don't know where is defined.

- May 26th 2011, 02:46 AMkinkong
T:X-->X is the contraction on X if there is a positive \alpha <1 such that d(tx,ty)\leqslant \alpha d(x,y)

- May 26th 2011, 02:50 AMgirdav
For the first question, prove by induction that if .

- May 26th 2011, 03:00 AMgirdav
For the second question we can put , and .