metric space is a set M together with a distance function p(z, y) tha (i) p(z,y) > 0 and (z,y)-0 if and only if y; (İİİ) plz, y) p(z, z) +pls, y) for all a, y,z in M. between elements r and y of the set M. The distance function must sa Let (M. p) be a metric space. A mapping T from M into M is called a contraction if for some constant a with 0 S a <1, and all r and y in M 3. Let С[0.1] denote the set of continuous functions f : [0, 1]-+ R with metric max If(t)--g(t) tejo.i Using 1.g in Co. I given by fe) 1 and g C(o.1 C0. 1] defined by 0 show that the mapping T: (Tx)(t) 1+r(s) ds is not a contraction mapping

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A: I have proved all three conditions gor norm

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A: (a) is correct

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A: Please check the answer in next step

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Q: pls explain to me step by step. pls dont skip any steps. thanks

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A: Answer

Q: c spaces. Show that X x Y and Y

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A: Given below the answer in details

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Q: (a) Consider the metric space 0 (i) if r 1.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.