On the Two-Dimensional Version of the Sperner Lemma and Brouwer's Theorem

• Autorzy: Eugeniusz Barcz
• Języki publikacji: EN

Abstrakty

EN

In this work the Brouwer fixed point theorem for a triangle wasproved by two methods based on the Sperner Lemma. One of the two proofs of Sperner's Lemma given in the paper was carried out using the so-called index(original abstract)

Słowa kluczowe

EN

Mathematics; Functional equation

PL

Matematyka; Równanie funkcyjne

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2022
• Tom: 36 (2)
• Strony: 106--114

Twórcy

autor

Eugeniusz Barcz

• University of Warmia and Mazury, Olsztyn, Poland

Bibliografia

• Barcz E., Local versions of Banach principle, their generalizations and applications, in: A. Lecko (ed.), Courrent Research in Mathematical and Computer Sciences, Wydawnictwo UWM, Olsztyn, 2017, pp. 41-53.
• Milnor J., Analytic proofs of the "Hairy Ball Theorem" and the Brouwer Fixed Point Theorem, Amer. Math. Monthly 85 (1978), no. 7, 521-524.
• Shashkin Yu. A., Fixed Points, MathematicalWorld, 2, AMS, Providence & MAA,Washington, 1991.
• Violette D., Applications du lemme de Sperner pour les triangles, Bulletin AMQ 46 (2006), no. 4, 12-19.

Identyfikatory

DOI

10.2478/amsil-2022-0004