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Every $f : [a, b] → [a, b]$ has a fixed point where $f$ is continuous. Deduce the intermediate value theorem.

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#real-analysis #banach-fixed-point
761
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Banach Contraction mapping of $\Phi(f)(x)=\int_0^x \frac{1}{1+f(t)^2}dt$ , find a fixed point.

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#integration #analysis #ordinary-differential-equations #banach-fixed-point
59
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Solve using succesive approximation methods

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#approximation #banach-fixed-point
74
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Contraction Banach theorem

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#multivariable-calculus #normed-spaces #banach-fixed-point
184
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Banach fixed-point theorem for a recursive functional equation

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#functional-analysis #metric-spaces #functional-equations #fixed-point-theorems #banach-fixed-point
1.9k
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Every 1-Lipschitz function in the closed unit ball has a fixed point

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#metric-spaces #lipschitz-functions #banach-fixed-point
62
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Banach Fixed Point Problem (Existence by showing contraction)

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#general-topology #banach-fixed-point
125
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Complete a proof that $F(x,y)$ is contracting.

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#real-analysis #multivariable-calculus #fixed-point-theorems #banach-fixed-point
338
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Problems with the Banach fixed point theorem

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#real-analysis #analysis #banach-fixed-point
176
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Finish a proof of existence and uniqueness for a nonlinear pde with initial conditions.

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#general-topology #partial-differential-equations #wave-equation #banach-fixed-point
2.9k
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Completeness can be omitted from Banach Fixed Point Theorem?

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#real-analysis #functional-analysis #metric-spaces #banach-fixed-point
89
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Changing the norm will affect a contraction?

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#real-analysis #functional-analysis #normed-spaces #banach-fixed-point #contraction-operator
193
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Example where Banach fix point theorem isn't valid

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#metric-spaces #banach-fixed-point
223
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Applying Extreme Value Theorem to prove existence of unique fixed point

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#real-analysis #banach-fixed-point #extreme-value-theorem
481
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Exercise on the Banach fixed-point theorem

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#functions #metric-spaces #banach-fixed-point

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