A Digital Version of the Kakutani Fixed Point Theorem for Convex-valued Multifunctions

DOI10.1016/S1571-0661(05)80066-0zbMath1264.68200MaRDI QIDQ4923385

Rueiher Tsaur, Michael B. Smyth

Publication date: 6 June 2013

Published in: Electronic Notes in Theoretical Computer Science (Search for Journal in Brave)

zbMATH Keywords

intersection graphsdigital convexityKakutani theoremdigital picturespower structuresalmost fixed-point property

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Fixed-point and coincidence theorems (topological aspects) (54H25) Planar graphs; geometric and topological aspects of graph theory (05C10)

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Cites Work

• Semi-metrics, closure spaces and digital topology
• The coordinate representation of a graph and \(n\)-universal graph of radius 1
• Isotone relations and the fixed point property for posets
• Contractible transformations do not change the homology groups of graphs
• Power structures
• Infinitary varieties of structures closed under the formation of complex structures
• ‘Continuous’ functions on digital pictures
• Finite approximation of stably compact spaces
• Fixed Points of Order Preserving Multifunctions
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