[Turkmath:657] DEU Seminerleri: Digital topology

[cenap ozel]

Degerli Liste uyeleri

16/09/2015 çcarsamba gunu Celal bayar Universitesinden Dr Ozgur EGE "Digital
Approximate Fixed Points and Universal Functions" baslikli bir konusma
verecektir.

Herkes davetlidir.

Selamlar ve iyi calismalar

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Ter: Dokuz Eylul Universitesi matematik Bolumu B206 Seminer salonu

tarih: 16/09/2015 saat 15.30

ozet:        Digital Approximate Fixed Points and Universal Functions

                        Ozgur EGE

Department of Mathematics, Celal Bayar University,
Muradiye, 45140, Manisa, Turkey
E-mail: ozgur.ege at cbu.edu.tr

Digital topology with algebraic properties is a growing area in computer
vision, image processing and fixed point theory.
 Many researchers have studied the properties of digital images using
topology and algebraic topology.
Azriel Rosenfeld introduced the notion of a digitally continuous function
between digital images and showed that although digital images need not
have fixed point properties analogous to those of
the Euclidean spaces modeled by the images, there often are approximate
fixed point properties of such images.
In this talk, we introduce additional results concerning approximate fixed
points of digitally continuous functions. We have shown that the
approximate fixed point property is
preserved by digital isomorphism and by digital retraction. Finally, we
present several results concerning the relationship between universal
functions and the approximate fixed point property (AFFP).

Keywords and phrases: Digital topology, digital image, fixed point.

2010 Mathematic Subject Classification: 55M20;68R10;68U10

References
[1] L. Boxer, Digitally continuous functions, Pattern Recognition Letters,
15, 833–839, 1994.
 [2] L. Boxer, A classical construction for the digital fundamental group,
Journal of Mathematical Imaging and Vision, 10, 51–62, 1999.
 [3] L. Boxer, Properties of digital homotopy, Journal of Mathematical
Imaging and Vision, 22, 19–26, 2005.
[4] O. Ege and I. Karaca, Fundamental properties of digital simplicial
homology groups, American Journal of Computer Technology and Application,
1(2), 25–42, 2013.
 [5] O. Ege and I. Karaca, Banach fixed point theorem for digital images,
Journal of Nonlinear Science and Applications, 8(3), 237–245, 2015.
 [6] O. Ege and I. Karaca, Digital homotopy fixed point theory, Comptes
Rendus Mathematique, In press, 2015.
 [7] S.-E. Han, Non-product property of the digital fundamental group,
Information Sciences, 171, 73–91, 2005.
[8] G.T. Herman, Oriented surfaces in digital spaces, CVGIP: Graphical
Models and Image Processing, 55, 381–396, 1993.
 [9] E. Khalimsky, Motion, deformation, and homotopy in finite spaces, in
Proceedings IEEE Intl. Conf. on Systems, Man, and Cybernetics, 227–234,
1987.
[10] T.Y. Kong, A digital fundamental group, Computers and Graphics, 13,
159–166, 1989.
 [11] A. Rosenfeld, Continuous functions on digital pictures, Pattern
Recognition Letters, 4, 177–184, 1986.
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