Results 1 to 10 of about 11,069 (184)
No bullying! A playful proof of Brouwer’s fixed-point theorem [PDF]
Journal of Mathematical Economics, 2018 We give an elementary proof of Brouwer's fixed-point theorem. The only mathematical prerequisite is a version of the Bolzano-Weierstrass theorem: a sequence in a compact subset of $n$-dimensional Euclidean space has a convergent subsequence with a limit ...
Mark Voorneveld
exaly +7 more sources
Brouwer Fixed Point Theorem for Simplexes [PDF]
Formalized Mathematics, 2011 In this article we prove the Brouwer fixed point theorem for an arbitrary simplex which is the convex hull of its n + 1 affinely indepedent vertices of εn.
Adam Naumowicz +35 more
core +4 more sources
A Brouwer fixed point theorem for graph endomorphisms [PDF]
Fixed Point Theory and Applications, 2012 We prove a Lefschetz formula for general simple graphs which equates the Lefschetz number L(T) of an endomorphism T with the sum of the degrees i(x) of simplices in G which are fixed by T.
Knill, Oliver
core +6 more sources
Variations on the Brouwer Fixed Point Theorem: A Survey
Mathematics, 2020 This paper surveys some recent simple proofs of various fixed point and existence theorems for continuous mappings in R n
Jean Mawhin
doaj +3 more sources
Brouwer Fixed Point Theorem in the General Case [PDF]
Formalized Mathematics, 2011 In this article we prove the Brouwer fixed point theorem for an arbitrary convex compact subset of εn with a non empty interior. This article is based on [15].Institute of Informatics, University of Białystok, PolandGrzegorz Bancerek.
Agata Darmochwał +21 more
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Traversable Wormholes and the Brouwer Fixed-Point Theorem [PDF]
Journal of Applied Mathematics and Physics, 2020 6 pages, 1 ...
Peter K F Kuhfittig
exaly +3 more sources
Spherical Designs via Brouwer Fixed Point Theorem [PDF]
SIAM Journal on Discrete Mathematics, 2010 17 ...
Andriy V. Bondarenko +1 more
exaly +4 more sources
Browder’s Theorem through Brouwer’s Fixed Point Theorem
The American Mathematical Monthly, 2023 One of the conclusions of Browder (1960) is a parametric version of Brouwer's Fixed Point Theorem, stating that for every continuous function $f : ([0,1] \times X) \to X$, where $X$ is a simplex in a Euclidean space, the set of fixed points of $f$, namely, the set $\{(t,x) \in [0,1] \times X \colon f(t,x) = x\}$, has a connected component whose ...
Eilon Solan, Omri N. Solan
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Existence of Solutions and Algorithm for a System of Variational Inequalities
Fixed Point Theory and Applications, 2010 We obtain some existence results for a system of variational inequalities (for short, denoted by SVI) by Brouwer fixed point theorem. We also establish the existence and uniqueness theorem using the projection technique for the SVI and suggest an ...
Yali Zhao +3 more
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The Brouwer Fixed Point Theorem Revisited [PDF]
, 2016 We revisit the investigation of the computational content of the Brouwer Fixed Point Theorem in [7], and answer the two open questions from that work. First, we show that the computational hardness is independent of the dimension, as long as it is greater than 1 (in [7] this was only established for dimension greater than 2).
Vasco Brattka +3 more
openaire +4 more sources