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

Présenté par : Étienne Ghys

Ege, Ozgur1 ; Karaca, Ismet2
1 Department of Mathematics, Celal Bayar University, Muradiye, Manisa, 45140, Turkey
2 Department of Mathematics, Ege University, Bornova, Izmir, 35100, Turkey
Comptes Rendus. Mathématique, Tome 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
Ege, Ozgur 1 ; Karaca, Ismet 2

1 Department of Mathematics, Celal Bayar University, Muradiye, Manisa, 45140, Turkey
2 Department of Mathematics, Ege University, Bornova, Izmir, 35100, Turkey 
@article{CRMATH_2015__353_11_1029_0,
     author = {Ege, Ozgur and Karaca, Ismet},
     title = {Digital homotopy fixed point theory},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1029--1033},
     publisher = {Elsevier},
     volume = {353},
     number = {11},
     year = {2015},
     doi = {10.1016/j.crma.2015.07.006},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2015.07.006/}
}
TY  - JOUR
AU  - Ege, Ozgur
AU  - Karaca, Ismet
TI  - Digital homotopy fixed point theory
JO  - Comptes Rendus. Mathématique
PY  - 2015
SP  - 1029
EP  - 1033
VL  - 353
IS  - 11
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2015.07.006/
DO  - 10.1016/j.crma.2015.07.006
LA  - en
ID  - CRMATH_2015__353_11_1029_0
ER  - 
%0 Journal Article
%A Ege, Ozgur
%A Karaca, Ismet
%T Digital homotopy fixed point theory
%J Comptes Rendus. Mathématique
%D 2015
%P 1029-1033
%V 353
%N 11
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2015.07.006/
%R 10.1016/j.crma.2015.07.006
%G en
%F CRMATH_2015__353_11_1029_0
Ege, Ozgur; Karaca, Ismet. Digital homotopy fixed point theory. Comptes Rendus. Mathématique, Tome 353 (2015) no. 11, pp. 1029-1033. doi : 10.1016/j.crma.2015.07.006. http://www.numdam.org/articles/10.1016/j.crma.2015.07.006/

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Cité par Sources :