Is There A Generalization Of Brouwer's Fixed Point Theorem?

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ANOTHER GENERALIZATION OF BROUWER'S FIXED POINT THEOREM

ANOTHER GENERALIZATION OF BROUWER'S FIXED POINT THEOREM DAVID HENDERSON AND G. R. LIVESAY The theorem proved here is naturally suggested by the following

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Disclaimer: I'm not a mathematician. Statement: Any continuous mapping f of a closed interval into itself...

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Banach fixed point theorem?

What are some applications of this theorem? I've already seen it in the proof of the Picard–Lindelöf theorem and the Inverse function theorem. So any applications besides those two would be good. Thanks!

Answer:

The same principle underlying Picard-Lindelof can be used to prove local existence and uniqueness for...

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Banach fixed point theorem?

(scalar version) Let Ф: Ą ---> Ą be a contraction with constant k <1 then there exist a unique fixed point X* = Ф(x*) must be Ą show that the contraction constant k is given by k = max |Ф' (ε) | (max &epsilon...

Answer:

I am sorry but such real analysis questions are not possible to answer on this site. This result is...

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Can you offer a geometrical proof of the 3D generalization of the Pythagorean Theorem?

Given a right tetrahedron, where the right angles of 3 right triangle faces share a common vertex, let A, B, C be the areas of those 3 right triangle faces, and D be the area of the 4th face. Then the 3D generalization of the Pythagorean theorem is:...

Answer:

Here is a sketch. Let's give names to the vertices. Let JKLM be your right tetrahedron, M being the...

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Who's afraid of Kurt Gödel?

Help show me that Gödel's theorem isn't that big of a deal. A while back, I was surprised by: Infinity--more precisely the axiom of infinity--stalks every page. This axiom says that the collection of all natural numbers exists as a set,...

Answer:

Just because some theorems are unprovable doesn't mean the entire field of logic is worthless. It just...

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Answer:

Answer Krasnoselskii fixed point theorem states that under certain sircumstances the operator has at...

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An Isosceles Right Triangle has _____________ (Line, Point or Both) Symmetry.?

I know that A right triangle has line symmetry, but does It have Point Symmetry? The Def. of Point Symmetry is Point of rotation (according to The Teacher). Point of Rotation: A figure in a plane has rotational symmetry if the figure can be mapped onto...

Answer:

A rotation of 0 degrees doesn't move or transform the figure at all. It's like sliding it by a vector...

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Ellipse: Find the fixed point?

If 'P' be a moving point on the ellipse x^2/25 + y^2/16 =1 in such a way that the tangent at 'P' intersect x = 25/3 at Q then circle on PQ as diameter passes through a fixed point.Find the fixed point.

Answer:

It is a known fact that if a point P on an ellipse (or hyperbola or parabola) has a tangent meeting...

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At what point does a generalization become a stereotype?

One of the strategies that we use to facilitate learning and understanding foreign (as in unknown) concepts is generalization and association. We create schemas or mental maps. I think this is a wonderful, effective, built-in tool. But I think that in...

Answer:

Wow! This is a thoughtful question and equally thoughtful answers. Stereotypes are generalizations,...

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