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Mapping, Contraction and Fixed-Point Theorem : Let T(x) = x^2 Show that T is a contraction on (0, 1/3] , but that T has no fixed point on this interval. Does this conflict Theorem 6.4? Explain.

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3. Let T(x) = x^2 Show that T is a contraction on (0, 1/3] , but that T has no fixed point on this interval. Does this conflict Theorem 6.4? Explain.

Note: We are using the book Methods of Real Analysis by Richard R. Goldberg.
This theorem 6.4 is in the page 159:
"Let be a complete metric space. If T is a contraction on , then there is one and only one point in such that . (This is often stated as "T has precisely one fixed point").
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Note: we are using the "Methods of Real Analysis by Richard R Goldberg

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Mapping, Contraction and Fixed-Point Theorem are investigated. The solution is detailed and well presented.

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3. Let Show that T is a contraction on (0. , but that T has no fixed point on this interval. Does this conflict Theorem 6.4? Explain.

Note: We are using the book Methods of Real Analysis by Richard R. Goldberg.
This theorem 6.4 is in the page 159:
"Let be a complete metric space. If T is a ...

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