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Digital Space-Type Fixed Point Theory and Its Applications

In: Advances in Metric Fixed Point Theory and Applications

Author

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  • Sang-Eon Han

    (Jeonbuk National University, Department of Mathematics Education, Institute of Pure and Applied Mathematics)

Abstract

The present paper, as a survey paper, studies the fixed point property (FPP, for brevity) and the almost fixed point property (AFPP, for short) for digital spaces whose structures are induced by a digital graph in terms of the Rosenfeld model (or digital metric space), the Khalimsky (K-, for brevity), or the (extended) Marcus-Wyse (M-, for short) topology. Furthermore, we also investigate various properties of digital isomorphic (or homeomorphic), digital homotopic, retract, and product properties of the FPP and the AFPP of them. This approach can be used in applied sciences such as some areas of pure and applied topologies, applied analysis, and computer science such as computer graphics, image processing, pattern recognition, mathematical morphology, artificial intelligence, and so forth. All digital spaces are assumed to be connected (or k-connected) unless stated otherwise.

Suggested Citation

  • Sang-Eon Han, 2021. "Digital Space-Type Fixed Point Theory and Its Applications," Springer Books, in: Yeol Je Cho & Mohamed Jleli & Mohammad Mursaleen & Bessem Samet & Calogero Vetro (ed.), Advances in Metric Fixed Point Theory and Applications, chapter 0, pages 85-109, Springer.
    • Handle: RePEc:spr:sprchp:978-981-33-6647-3_5
    DOI: 10.1007/978-981-33-6647-3_5
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