Digital Space-Type Fixed Point Theory and Its Applications

Sang-Eon Han ()
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Sang-Eon Han: Jeonbuk National University, Department of Mathematics Education, Institute of Pure and Applied Mathematics

Chapter Chapter 5 in Advances in Metric Fixed Point Theory and Applications, 2021, pp 85-109 from Springer

Abstract: 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.

Keywords: (Almost) Fixed point property; Marcus Wyse topological space; Digital metric space; Khalimsky topological spaces; digital contractibility (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-33-6647-3_5

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DOI: 10.1007/978-981-33-6647-3_5

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