On the two-dimensional version of the Sperner Lemma and Brouwer's theorem

Eugeniusz Barcz

Published: 2022-09-08

Vol. 36 No. 2 (2022)

On the two-dimensional version of the Sperner Lemma and Brouwer's theorem

Eugeniusz Barcz

Abstract

In this work the Brouwer fixed point theorem for a triangle was proved 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.

Keywords:

Sperner’s Lemma , Brouwer’s theorem , retraction , fixed-point property

Download files

PDF

Citation rules

Barcz, E. (2022). On the two-dimensional version of the Sperner Lemma and Brouwer’s theorem. Annales Mathematicae Silesianae, 36(2), 106–114. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14550

Similar Articles

Wojciech Surówka, A discrete form of Jordan curve theorem , Annales Mathematicae Silesianae: Vol. 7 (1993)
Binayak S. Choudhury, Nikhilesh Metiya, Sunirmal Kundu, Debashis Khatua, Existence, data dependence and stability of fixed points of multivalued maps in incomplete metric spaces , Annales Mathematicae Silesianae: Vol. 37 No. 1 (2023)
Valeriu Popa, Alina-Mihaela Patriciu, Fixed point theorems for two pairs of mappings satisfying a new type of common limit range property in G_p metric spaces , Annales Mathematicae Silesianae: Vol. 32 (2018)
Mohammad Asim, Mohammad Imdad, Fixed point and best proximity point results in PIV-S-metric spaces , Annales Mathematicae Silesianae: 2024: Online First
Eugeniusz Barcz, A new proof and consequences of the fixed point theorem of Matkowski , Annales Mathematicae Silesianae: Vol. 35 No. 2 (2021)
Valeriu Popa, Alina-Mihaela Patriciu, Altering distance and common fixed points for hybrid mappings under implicit relations and applications , Annales Mathematicae Silesianae: Vol. 28 (2014)
Zofia Muzyczka, On functional-differential equations with advancing argument , Annales Mathematicae Silesianae: Vol. 2 (1986)
Valeriu Popa, A general fixed point theorem for implicit cyclic multi-valued contraction mappings , Annales Mathematicae Silesianae: Vol. 29 (2015)
Mian Bahadur Zada, Muhammad Sarwar, Fixed point results satisfying rational type contractive conditions in complex valued metric spaces – revisited , Annales Mathematicae Silesianae: Vol. 31 (2017)
Valeriu Popa, A general fixed point theorem for two pairs of absorbing mappings in Gp-metric spaces , Annales Mathematicae Silesianae: Vol. 34 No. 2 (2020)

1 2 3 4 5 6 7 8 9 10 > >>

You may also start an advanced similarity search for this article.

References

E. Barcz, 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.
Google Scholar

J. Milnor, Analytic proofs of the “Hairy Ball Theorem” and the Brouwer Fixed Point Theorem, Amer. Math. Monthly 85 (1978), no. 7, 521–524.
Google Scholar

Yu.A. Shashkin, Fixed Points, MathematicalWorld, 2, AMS, Providence & MAA,Washington, 1991.
Google Scholar

D. Violette, Applications du lemme de Sperner pour les triangles, Bulletin AMQ 46 (2006), no. 4, 12–19.
Google Scholar

Vol. 36 No. 2 (2022)
Published: 2022-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

Submit