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Review

Variations on the Brouwer Fixed Point Theorem: A Survey

Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, chemin du Cyclotron, 2, 1348 Louvain-la-Neuve, Belgium
Mathematics 2020, 8(4), 501; https://doi.org/10.3390/math8040501
Submission received: 25 February 2020 / Revised: 20 March 2020 / Accepted: 21 March 2020 / Published: 2 April 2020
(This article belongs to the Special Issue Nonlinear Functional Analysis and Its Applications)

Abstract

This paper surveys some recent simple proofs of various fixed point and existence theorems for continuous mappings in R n . 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.
Keywords: Brouwer fixed point theorem; Hamadard theorem; Poincaré–miranda theorem Brouwer fixed point theorem; Hamadard theorem; Poincaré–miranda theorem

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MDPI and ACS Style

Mawhin, J. Variations on the Brouwer Fixed Point Theorem: A Survey. Mathematics 2020, 8, 501. https://doi.org/10.3390/math8040501

AMA Style

Mawhin J. Variations on the Brouwer Fixed Point Theorem: A Survey. Mathematics. 2020; 8(4):501. https://doi.org/10.3390/math8040501

Chicago/Turabian Style

Mawhin, Jean. 2020. "Variations on the Brouwer Fixed Point Theorem: A Survey" Mathematics 8, no. 4: 501. https://doi.org/10.3390/math8040501

APA Style

Mawhin, J. (2020). Variations on the Brouwer Fixed Point Theorem: A Survey. Mathematics, 8(4), 501. https://doi.org/10.3390/math8040501

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