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Fixed Point Sets of Digital Curves and Digital Surfaces

Author

Listed:
  • Sang-Eon Han

    (Department of Mathematics Education, Institute of Pure and Applied Mathematics, Jeonbuk National University, Jeonju-City Jeonbuk 54896, Korea)

Abstract

Given a digital image (or digital object) ( X , k ) , we address some unsolved problems related to the study of fixed point sets of k -continuous self-maps of ( X , k ) from the viewpoints of digital curve and digital surface theory. Consider two simple closed k -curves with l i elements in Z n , i ∈ { 1 , 2 } , l 1 ⪈ l 2 ≥ 4 . After initially formulating an alignment of fixed point sets of a digital wedge of these curves, we prove that perfectness of it depends on the numbers l i , i ∈ { 1 , 2 } , instead of the k -adjacency. Furthermore, given digital k -surfaces, we also study an alignment of fixed point sets of digital k -surfaces and digital wedges of them. Finally, given a digital image which is not perfect, we explore a certain condition that makes it perfect. In this paper, each digital image ( X , k ) is assumed to be k -connected and X ♯ ≥ 2 unless stated otherwise.

Suggested Citation

  • Sang-Eon Han, 2020. "Fixed Point Sets of Digital Curves and Digital Surfaces," Mathematics, MDPI, vol. 8(11), pages 1-25, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1896-:d:438059
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    References listed on IDEAS

    as
    1. Han, Sang-Eon, 2019. "Estimation of the complexity of a digital image from the viewpoint of fixed point theory," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 236-248.
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    Cited by:

    1. Yu Song & Chenfei Qian & Susan Pickard, 2021. "Age-Related Digital Divide during the COVID-19 Pandemic in China," IJERPH, MDPI, vol. 18(21), pages 1-13, October.
    2. Sang-Eon Han, 2021. "Discrete Group Actions on Digital Objects and Fixed Point Sets by Iso k (·)-Actions," Mathematics, MDPI, vol. 9(3), pages 1-25, February.

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    1. Sang-Eon Han, 2021. "Discrete Group Actions on Digital Objects and Fixed Point Sets by Iso k (·)-Actions," Mathematics, MDPI, vol. 9(3), pages 1-25, February.
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