Published March 3, 2023
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Brouwer fixed point theorem in strictly star-shaped sets
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- 1. Nicolaus Copernicus University
- 2. Sidi-Bel-Abbes University
Description
In this note, we show that the Brouwer fixed point theorem in open strictly star-shaped sets is equivalent to a number of results closely related to the Euclidean spaces.
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References
- A. Boulkhemair and A. Chakib, On a shape derivative formula with respect to convex domains. J. Convex Anal. 21, No. 1, (2014), 67-87
- P. Bohl, Ueber die Bewegung eines mechanischen Systems in der Nähe einer Gleichgewichtslage. J. Reine Angew. Math. 127, (1904), 179-276.
- L. E.J. Brouwer, Über Abbildung von Mannigfaltigkeiten. (German) Math. Ann. 71 (1911), no. 1, 97?115.
- G. Dinca and J. Mawhin, Brouwer Degree. The Core of Nonlinear Analysis. Progress in Nonlinear Di?erential Equations and Their Applications 95. Cham: Birkhäuser 2021.
- C. González, A. Jiménez-Melado, and E. Llorens-Fuster, A Mönch type ?xed point theorem under the interior condition, J. Math. Anal. Appl. 352 (2009), 816?821.
- L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, Springer, New York, 2006.
- J. Hadamard, Note sur quelques applications de l'indice de Kronecker. In Jules Tannery: Introduction à la théorie des fonctions d'une variable (Volume 2), 2nd edition, A. Hermann & Fils, (1910), 437-477.
- A. Hatcher, Algebraic Topology. Cambridge University Press, Cambridge 2002
- S. Kakutani, A generalization of Brouwer's ?xed point theorem. Duke Math. J. 8, (1941), 457-459
- B. Knaster, K. Kuratowski and S. und Mazurkiewicz, Ein Beweis des Fixpunktsatzes füur n-Dimensionale Simplexe. Fund. Math. 14, (1929), 132-137.
- R.B. Kellogg, T.Y. Li and J. Yorke, A constructive proof of the Brouwer ?xed-point theorem and computational results. SIAM J. Numer. Anal. 13, (1976), 473-483.
- J. Milnor, Analytic proofs of the ?Hairy Ball Theorem? and the Brouwer. Fixed Point Theorem Am. Math. Monthly 85, (1978), 525-527.
- S. Park, Ninety years of the Brouwer ?xed point theorem, Vietnam J. Math. 27 (1999), 187?222
- H. Poincaré, Sur certaines solutions particulidres du problbme des trois corps, BuIl. Astronomique 1 (1884) 65-14, in Oeuvres de H. Poincaré, t. VII, Gautier-Villars, Paris, (1928), 253-261.
- J. F. Nash, Equilibrium points in n-person games, Pro.the United States of America 36 (1950), 48-49.
- J. F. Nash, Noncooperative games, Annals of Mathematics, 54, (1951), 289-295.
- A. Jiménez-Melado and C. H. Morales, Fixed point theorems under the interior condition, Proc. Amer. Math. Soc. 134 (2006), 501?507.
- E. Zeidler, Nonlinear Functional Analysis and Its Applications I. Springer, New York 1986.