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Biography

Sang-Eon Han
Prof. Sang-Eon Han
Chonbuk National University, Republic of Korea
Title:
FIXED POINT THEORY FOR DIGITAL SPACES ASSOCIATED WITH KHALIMSKY AND MW-TOPOLOGY
Abstract:

In this talk, we studies the fixed point theory and the almost fixed point theory from the viewpoint of digital topology associated with Khalimsky and Marcus-Wyse topology. Based on a digital version of the Banach contraction principle [1], in digital topology, we say that a digital image (X, k) has the fixed point property if every k-continuous map f : (X, k) → (X, k) has a fixed point x ∈ X, i.e. f(x) = x. Motivated by the formal research into the fixed point property, we have some intrinsic features in digital digital versions of both fixed point property and the almost fixed point property [1, 2, 3, 4, 5, 6, 7]. This approach can be used in certain areas in both computer science and applied sciences.


References
[1] L.E.J. Brouwer, Uber Abbildung von Mannigfaltigkeiten, Math. Ann. 71
(1912), 97-115.
[2] S.-E. Han, Non-product property of the digital fundamental group, Information
Sciences 171(1-3) (2005) 73-91.
[3] S.-E. Han, The k-homotopic thinning and a torus-like digital image in Z
n,Journal of Mathematical Imaging and Vision 31(1) (2008) 1-16.
[4] S.-E. Han, Banach fixed point theorem from the viewpoint of digital topology,
Journal of Nonlinear Sciences and Applications 9(3) (2016) 895-905.
[5] S.-E. Han, Almost fixed point property for digital spaces associated with
Marcus-Wyse topological spaces, Journal of Nonlinear Sciences and Applications
10 (2017) 34-47.
[6] S. Lefschetz, Intersections and transformations of complexes and manifolds.
Trans. Amer. Math. Soc. 28 (1) (1926) 1-49.
[7] A. Rosenfeld, A. Rosenfeld, Digital topology, Amer. Math. Monthly, 86 (1979)
76-87.

Biography:
He has accomplished his doctoral degree of science at Chonnam National University in 1988. He worked at StanfordUniversity as a visiting scholar in 1998. Now he is a full Professor at Department of Mathematics Education in Chonbuk National University. He have studied pure and applied mathematics including the following areas: Algebraic topology, combinatorial topology, general topology, digital topology such as Khalimsky and Marcus-Wyse, space set topology, computational topology, digital geometry and so on. Recently, he developed many useful tools related to digitizations of Hausdorff topological spaces in terms of K-and MA-digitization and so forth. Furthermore, he settled many problems associated with fixed point theory for digital spaces. As a result, he has published 150 mathematical journal papers and 12 books (for more details, see the website:http://sehan.jbnu.ac.kr/). In particular, he developed digital covering theory and high dimensional digital surface theory which were published in Information Sciences and JMIV and so on. He has also delivered invited talks in many international conferences held in 50 countries. He has also organized many times international conferences named by IWAT (International Workshop on Applied Topology).
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