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.
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We don't know where is defined.
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)
For the first question, prove by induction that if .
For the second question we can put , and .
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