Variations on the Brouwer Fixed Point Theorem: A Survey

Mawhin, Jean
(2020) Mathematics — Vol. 8, n° 4, p. 501 (2020)

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  • Mawhin, Jeanorcid-logoUCLouvain
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Abstract
This paper surveys some recent simple proofs of various fixed point and existence theorems for continuous mappings in Rn. The main tools are basic facts of the exterior calculus and the use of retractions. The special case of holomorphic functions is considered, based only on the Cauchy integral theorem.
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Mawhin, J. (2020). Variations on the Brouwer Fixed Point Theorem: A Survey. Mathematics, 8(4), 501. https://doi.org/10.3390/math8040501 (Original work published 2020)