The Schauder fixed-point theorem is an extension of the Brouwer fixed-point theorem to locally convex topological vector spaces, which may be of infinite...

Poincaré–Birkhoff theorem proves the existence of two fixed points Ryll-Nardzewski fixed-point theorem Schauder fixed-point theorem Topological degree...

theorems for partial differential equations. The first result in the field was the Schauder fixed-point theorem, proved in 1930 by Juliusz Schauder (a...

Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f...

methods in nonlinear analysis. Banach–Schauder theorem Schauder basis Schauder estimates Schauder fixed point theorem List of Polish mathematicians Kuratowski...

Schauder theorem may refer to: Schauder fixed-point theorem A result about compact operators, see Compact operator § Important properties This disambiguation...

representation theorem (functional analysis, Hilbert space) Schauder fixed-point theorem (functional analysis) Schwartz kernel theorem (generalized functions)...

Brouwer fixed-point theorem, every compact and convex subset of a Euclidean space has the FPP. More generally, according to the Schauder-Tychonoff fixed point...

journal. Lomonosov (1973) gave a very short proof using the Schauder fixed point theorem that if the operator T {\displaystyle T} on a Banach space commutes...

"Lomonosov's spectacular invariant subspace theorem". Lomonosov gives a very short proof, using the Schauder fixed point theorem, that if a bounded linear operator...

invariant-direction theorem, named after G. D. Birkhoff and O. D. Kellogg, is a generalization of the Brouwer fixed-point theorem. The theorem states that: Let...

Hahn–Banach theorem, the Banach–Steinhaus theorem, the Banach–Mazur game, the Banach–Alaoglu theorem, and the Banach fixed-point theorem. Stefan Banach...

Leray-Schauder fixed point theorem but establishing only the fixed point without the hyperbolicity. Work of Dennis Sullivan later showed that the fixed point...

possible to prove that solutions exist using the continuity method or a fixed point theorem. A priori estimates were introduced and named by Sergei Natanovich...

murdered in prison by the Gestapo, Warsaw Juliusz Schauder 1899–1943 Polish Schauder fixed point theorem, Schauder basis Jewish executed by the Gestapo, Lviv...

Schauder, Polish mathematician known for Schauder basis, Schauder fixed-point theorem, Schauder estimates, Banach–Schauder theorem and Faber-Schauder...

invertibility of the derivative at a point is sufficient for a map to be locally invertible, the Nash–Moser theorem requires the derivative to be invertible...

Banach–Alaoglu theorem Banach–Mazur compactum Banach–Mazur game Banach–Mazur theorem Banach–Ruziewicz problem Banach-Saks theorem Banach-Schauder theorem Banach–Steinhaus...

Orthonormal basis Schauder basis Basis (universal algebra) Basis of a matroid Generating set of an ideal: Gröbner basis Hilbert's basis theorem Generating set...

differential equations and the topological methods used there (fixed-point theorems, Leray-Schauder theory) and methods of nonlinear functional analysis. As...

gij. So it is automatic from elliptic regularity, and in particular the Schauder estimates, that if g is C2 and Ric(g) is Ck, α relative to a harmonic coordinate...

Math. 17 (1964), 101–134. Fan, Ky. A generalization of Tychonoff's fixed point theorem. Math. Ann. 142 (1960), 305–310. Fan, Ky. A minimax inequality and...

between Banach spaces is compact if and only if its adjoint is compact (Schauder's theorem). If T : X → Y {\displaystyle T:X\to Y} is bounded and compact, then:...

contractions, fixed-point theorems for monotone operators and a combination of the Schauder fixed-point and contraction mapping theorems that was the genesis...

B_{V}}\sum _{w\in B_{W}}B(v,w)(v\otimes w)} making these maps similar to a Schauder basis for the vector space Hom ( V , W ; F ) {\displaystyle {\text{Hom}}(V...

considered, which using Zorn's Lemma, implies it admits a countably infinite Schauder basis rather than an orthonormal basis in the sense of linear algebra (Hamel...

Fréchet derivative is a completely continuous operator and for Rothe's fixed point theorem, proven in 1937. In 1978 a collection of papers was published in...

Ryll-Nardzewski Ryll-Nardzewski fixed-point theorem. Schauder Schauder basis. Schatten Schatten class selection Michael selection theorem. self-adjoint A self-adjoint...