Fixed point property for digital spaces

Volume 10, Issue 5, pp 2510--2523 http://dx.doi.org/10.22436/jnsa.010.05.20

Publication Date: May 25, 2017 Submission Date: January 19, 2017

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Authors

Sang-Eon Han - Department of Mathematics Education, Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju-City Jeonbuk, 561-756, Republic of Korea.

Abstract

The paper compares the fixed point property (FPP for short) of a compact Euclidean plane with its digital versions associated with Khalimsky and Marcus-Wyse topology. More precisely, by using a Khalimsky and a Marcus-Wyse topological digitization, the paper studies digital versions of the FPP for Euclidean topological spaces. Besides, motivated by the digital homotopy fixed point property (DHFP for brevity) [O. Ege, I. Karaca, C. R. Math. Acad. Sci. Paris, 353 (2015), 1029–1033], the present paper establishes the digital homotopy almost fixed point property (DHAFP for short) which is more generalized than the DHFP. Moreover, the present paper corrects some errors in [O. Ege, I. Karaca, C. R. Math. Acad. Sci. Paris, 353 (2015), 1029–1033] and improves it.

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Keywords

• Digital space
• digitization
• Khalimsky topology
• Marcus-Wyse topology
• fixed point property
• digital homotopy almost fixed point property
• almost fixed point property.

MSC

•  55N35
•  55M20
•  68R10
•  68U05

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