Comptes Rendus
no. 11
Topology/Computer science
Digital homotopy fixed point theory
[Théorie du point fixe pour les homotopies digitales]

Présenté par : Étienne Ghys

Ozgur Ege1 ; Ismet Karaca2
1 Department of Mathematics, Celal Bayar University, Muradiye, Manisa, 45140, Turkey
2 Department of Mathematics, Ege University, Bornova, Izmir, 35100, Turkey
Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 1029-1033.

Nous démontrons de nouveaux résultats sur les images digitales dont les homotopies digitales entre deux transformations continues de l'image possèdent un chemin de points fixes. Ceci conduit à une théorie du point fixe des homotopies digitales, dont nous donnons une application sur une image digitale.

In this paper, we construct a framework which is called the digital homotopy fixed point theory. We get new results associating digital homotopy and fixed point theory. We also give an application on this theory.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.07.006
Ozgur Ege 1 ; Ismet Karaca 2

1 Department of Mathematics, Celal Bayar University, Muradiye, Manisa, 45140, Turkey
2 Department of Mathematics, Ege University, Bornova, Izmir, 35100, Turkey 
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Ozgur Ege; Ismet Karaca. Digital homotopy fixed point theory. Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 1029-1033. doi : 10.1016/j.crma.2015.07.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.07.006/

[1] L. Boxer Digitally continuous functions, Pattern Recognit. Lett., Volume 15 (1994), pp. 833-839

[2] L. Boxer A classical construction for the digital fundamental group, J. Math. Imaging Vis., Volume 10 (1999), pp. 51-62

[3] L. Boxer Properties of digital homotopy, J. Math. Imaging Vis., Volume 22 (2005), pp. 19-26

[4] L. Boxer Homotopy properties of sphere-like digital images, J. Math. Imaging Vis., Volume 24 (2006), pp. 167-175

[5] L. Boxer Digital products, wedges and covering spaces, J. Math. Imaging Vis., Volume 25 (2006), pp. 159-171

[6] L. Boxer Fundamental groups of unbounded digital images, J. Math. Imaging Vis., Volume 27 (2007), pp. 121-127

[7] O. Ege; I. Karaca Fundamental properties of simplicial homology groups for digital images, Amer. J. Comput. Technol. Appl., Volume 1 (2013) no. 2, pp. 25-42

[8] O. Ege; I. Karaca Lefschetz fixed point theorem for digital images, Fixed Point Theory Appl., Volume 2013 (2013) no. 253

[9] O. Ege; I. Karaca Applications of the Lefschetz number to digital images, Bull. Belg. Math. Soc. Simon Stevin, Volume 21 (2014) no. 5, pp. 823-839

[10] O. Ege; I. Karaca Banach fixed point theorem for digital images, J. Nonlinear Sci. Appl., Volume 8 (2015) no. 3, pp. 237-245

[11] S.E. Han An extended digital (k0,k1)-continuity, J. Appl. Math. Comput., Volume 16 (2004) no. 1–2, pp. 445-452

[12] S.E. Han Non-product property of the digital fundamental group, Inf. Sci., Volume 171 (2005), pp. 73-91

[13] G.T. Herman Oriented surfaces in digital spaces, CVGIP, Graph. Models Image Process., Volume 55 (1993), pp. 381-396

[14] I. Karaca; O. Ege Some results on simplicial homology groups of 2D digital images, Int. J. Inf. Comput. Sci., Volume 1 (2012) no. 8, pp. 198-203

[15] M. Szymik Homotopies and the universal fixed point property, Order (2014) | DOI

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