Multivalued Maps As a Tool in Modeling and Rigorous Numerics
نویسنده
چکیده
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 and differential inclusions; (3) Computing homology of maps; (4) Conley index methods in chaotic dynamics; (5) Digital imaging and computer vision. We briefly recall the history 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 the more recent applications (3), (4), and (5), where a multivalued map plays a role of a numerical tool.
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