Variations on the Brouwer Fixed Point Theorem: A Survey

Jean Mawhin
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Jean Mawhin: Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, chemin du Cyclotron, 2, 1348 Louvain-la-Neuve, Belgium

Mathematics, 2020, vol. 8, issue 4, 1-14

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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