Abstract.
Applications of the fixed point theory of multivalued maps can be classified into several areas: (1) Game theory and mathematical economics; (2) Discontinuous differential equations, differential inclusions, and optimal control; (3) Computing homology of maps; (4) Computer assisted proofs in dynamics; (5) Digital imaging. We give an overview of the most classical and well developed areas of applications (1) and (2), where a multivalued map is used as a generalization of a single-valued continuous map, and we survey more recent applications (3), (4), and (5), where multivalued maps play the role of a numerical tool.
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Dedicated to Felix Browder on his 80th birthday
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Kaczynski, T. Multivalued maps as a tool in modeling and rigorous numerics. J. fixed point theory appl. 4, 151–176 (2008). https://doi.org/10.1007/s11784-008-0089-y
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DOI: https://doi.org/10.1007/s11784-008-0089-y