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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 wikiPageRevisionID "605716941".
- 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:Functional_analysis.
- Fixed-point_theorems_in_infinite-dimensional_spaces subject Category:Mathematical_and_quantitative_methods_(economics).
- Fixed-point_theorems_in_infinite-dimensional_spaces subject Category:Theorems_in_topology.
- Fixed-point_theorems_in_infinite-dimensional_spaces type Abstraction100002137.
- Fixed-point_theorems_in_infinite-dimensional_spaces type Communication100033020.
- Fixed-point_theorems_in_infinite-dimensional_spaces type Fixed-pointTheorems.
- Fixed-point_theorems_in_infinite-dimensional_spaces type Message106598915.
- Fixed-point_theorems_in_infinite-dimensional_spaces type Proposition106750804.
- Fixed-point_theorems_in_infinite-dimensional_spaces type Statement106722453.
- Fixed-point_theorems_in_infinite-dimensional_spaces type Theorem106752293.
- Fixed-point_theorems_in_infinite-dimensional_spaces type TheoremsInTopology.
- 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 Q17089994.
- Fixed-point_theorems_in_infinite-dimensional_spaces sameAs Q17089994.
- Fixed-point_theorems_in_infinite-dimensional_spaces sameAs Fixed-point_theorems_in_infinite-dimensional_spaces.
- Fixed-point_theorems_in_infinite-dimensional_spaces wasDerivedFrom Fixed-point_theorems_in_infinite-dimensional_spaces?oldid=605716941.
- Fixed-point_theorems_in_infinite-dimensional_spaces isPrimaryTopicOf Fixed-point_theorems_in_infinite-dimensional_spaces.