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- Fixed-point_theorems_in_infinite-dimensional_spaces abstract "In mathematics, a number of fixed-point theorems in infinite-dimensional spaces generalise the Brouwer fixed-point theorem. They have applications, for example, to the proof of existence theorems for partial differential equations. The first result in the field was the Schauder fixed-point theorem, proved in 1930 by Juliusz Schauder (a previous result in a different vein, the Banach fixed-point theorem for contraction mappings in complete metric spaces was proved in 1922). Quite a number of further results followed. One way in which fixed-point theorems of this kind have had a larger influence on mathematics as a whole has been that one approach is to try to carry over methods of algebraic topology, first proved for finite simplicial complexes, to spaces of infinite dimension. For example, the research of Jean Leray who founded sheaf theory came out of efforts to extend Schauder's work.Schauder fixed-point theorem: Let C be a nonempty closed convex subset of a Banach space V, if f : C → C is continuous with a compact image, then f has a fixed point.Tikhonov (Tychonoff) fixed point theorem: Let V be a locally convex topological vector space, for any non-empty compact convex set X in V, any continuous function f : X → X has a fixed point.Other results include the Markov–Kakutani fixed-point theorem (1936-1938) and the Ryll-Nardzewski fixed-point theorem (1967) for continuous affine self-mappings of compact convex sets, as well as the Earle–Hamilton fixed-point theorem (1968) for holomorphic self-mappings of open domains.Kakutani's fixed-point theorem: Every correspondence that maps a compact convex subset of a locally convex space into itself with a closed graph and convex nonempty images has a fixed point.".
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageExternalLink TychonoffFixedPointTheorem.html.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageID "638186".
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageLength "2838".
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageOutDegree "30".
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageRevisionID "641999717".
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Algebraic_topology.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Banach_fixed-point_theorem.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Banach_space.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Brouwer_fixed-point_theorem.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Category:Fixed-point_theorems.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Category:Mathematical_and_quantitative_methods_(economics).
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Closed_set.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Compact_set.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Compact_space.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Continuous_function.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Contraction_mapping.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Convex_set.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Earle–Hamilton_fixed-point_theorem.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Empty_set.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Existence_theorem.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Fixed_point_(mathematics).
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink James_Dugundji.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Jean_Leray.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Juliusz_Schauder.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Kakutani_fixed-point_theorem.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Kakutani_fixed_point_theorem.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Locally_convex_topological_vector_space.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Markov–Kakutani_fixed-point_theorem.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Mathematics.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Metric_space.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Metric_spaces.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Nonempty.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Partial_differential_equation.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Ryll-Nardzewski_fixed-point_theorem.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Schauder_fixed-point_theorem.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Schauder_fixed_point_theorem.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Sheaf_(mathematics).
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Sheaf_theory.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Simplicial_complex.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLink Topological_degree_theory.
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLinkText "Fixed-point theorems in infinite-dimensional spaces".
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLinkText "Schauder's fixed-point theorem".
- Fixed-point_theorems_in_infinite-dimensional_spaces wikiPageWikiLinkText "fixed-point theorems in infinite-dimensional spaces".
- Fixed-point_theorems_in_infinite-dimensional_spaces hasPhotoCollection Fixed-point_theorems_in_infinite-dimensional_spaces.
- Fixed-point_theorems_in_infinite-dimensional_spaces subject Category:Fixed-point_theorems.
- Fixed-point_theorems_in_infinite-dimensional_spaces subject Category:Mathematical_and_quantitative_methods_(economics).
- Fixed-point_theorems_in_infinite-dimensional_spaces type Function.
- Fixed-point_theorems_in_infinite-dimensional_spaces type Theorem.
- Fixed-point_theorems_in_infinite-dimensional_spaces comment "In mathematics, a number of fixed-point theorems in infinite-dimensional spaces generalise the Brouwer fixed-point theorem. They have applications, for example, to the proof of existence theorems for partial differential equations. The first result in the field was the Schauder fixed-point theorem, proved in 1930 by Juliusz Schauder (a previous result in a different vein, the Banach fixed-point theorem for contraction mappings in complete metric spaces was proved in 1922).".
- Fixed-point_theorems_in_infinite-dimensional_spaces label "Fixed-point theorems in infinite-dimensional spaces".
- Fixed-point_theorems_in_infinite-dimensional_spaces sameAs 無限次元空間における不動点定理.
- Fixed-point_theorems_in_infinite-dimensional_spaces sameAs Q17089994.
- Fixed-point_theorems_in_infinite-dimensional_spaces sameAs Q17089994.
- Fixed-point_theorems_in_infinite-dimensional_spaces wasDerivedFrom Fixed-point_theorems_in_infinite-dimensional_spaces?oldid=641999717.
- Fixed-point_theorems_in_infinite-dimensional_spaces isPrimaryTopicOf Fixed-point_theorems_in_infinite-dimensional_spaces.