Question: show full steps and explanations Let T:C([0,1])C([0,1]) be a function defined as Tf(x)=0xf(t)dt where C([0,1]) is the metric space of all continuous real valued functions

show full steps and explanations Let

show full steps and explanations

Let T:C([0,1])C([0,1]) be a function defined as Tf(x)=0xf(t)dt where C([0,1]) is the metric space of all continuous real valued functions defined on [0,1] and d(f,g)=sup0x1f(t)g(t)=fg. Show that: (i) T is NOT a contraction, (ii) T has a unique fixed point

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