pls explain to me step by step. pls write clearly and dont skip any steps. thanks
To test the contraction mapping property for the same operator T in two different settings . (C[0,1] and C[0,1/2] )
By definition, a contractive map T: X ->X has the property that it reduces distances between pairs of point in X. If T is a contraction mapping, the fixed point therorem says there is at least one fixed point for the mapping T. In other words, there exists a point x in T such that T(x)=x
In the first part of the problem, we show that the mapT defined on C[0,1] with the supremum distance is NOT a contract...
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