In mathematical analysis, the Kakutani fixed-point theorem is a fixed-point theorem for set-valued functions. It provides sufficient conditions for 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...

space Kakutani fixed-point theorem Kleene fixed-point theorem Knaster–Tarski theorem Lefschetz fixed-point theorem Nielsen fixed-point theorem Poincaré–Birkhoff...

In mathematics, the Markov–Kakutani fixed-point theorem, named after Andrey Markov and Shizuo Kakutani, states that a commuting family of continuous affine...

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

equilibrium of a game is a fixed point of the game's best response correspondence. John Nash exploited the Kakutani fixed-point theorem for his seminal paper...

In mathematics, a number of fixed-point theorems in infinite-dimensional spaces generalise the Brouwer fixed-point theorem. They have applications, for...

critic for The New York Times. The Kakutani fixed-point theorem is a generalization of Brouwer's fixed-point theorem, holding for generalized correspondences...

mathematics, Kakutani's theorem may refer to: the Kakutani fixed-point theorem, a fixed-point theorem for set-valued functions; Kakutani's theorem (geometry):...

the Kakutani fixed-point theorem in his 1950 paper to prove existence of equilibria. His 1951 paper used the simpler Brouwer fixed-point theorem for the...

there is a point y in X such that y ∈ F ( y ) {\displaystyle y\in F(y)} . This is a discrete analogue of the Kakutani fixed-point theorem, and the function...

critic Shizuo Kakutani (1911–2004), Japanese-American mathematician Kakutani fixed-point theorem This page lists people with the surname Kakutani. If an internal...

Markov-Kakutani fixed-point theorem - abelian semigroup of continuous affine self-maps on compact convex set in a topological vector space has a fixed point...

to do so. Envelope theorem Brouwer fixed point theorem Kakutani fixed point theorem for correspondences Michael selection theorem Ok, Efe (2007). Real...

be guaranteed; this is by Glicksberg's generalization of the Kakutani fixed point theorem. The class of continuous games is for this reason usually defined...

of PPAD-complete problems. Sperner's lemma Brouwer fixed-point theorem Kakutani fixed-point theorem Nash equilibrium Core of Balanced Games Fisher market...

unit circle leaves the point (0,0) fixed. Notice that the Kakutani theorem does not assert that there exists exactly one fixed point. Reflecting the unit disk...

proved from Sperner's lemma and can be used to prove the Brouwer fixed-point theorem. Let Δ n − 1 {\displaystyle \Delta _{n-1}} be an ( n − 1 ) {\displaystyle...

differential inclusions and related subjects as game theory, where the Kakutani fixed-point theorem for set-valued functions has been applied to prove existence...

equations) Markov tree Markov's theorem Markov time Markov brothers' inequality Markov–Krein theorem Markov–Kakutani fixed-point theorem Quantum Markov semigroup...

operator Discontinuous linear map Kakutani fixed-point theorem – Fixed-point theorem for set-valued functions Open mapping theorem (functional analysis) – Condition...

Brouwer fixed-point theorem to the unit ball in H. The existence of such counter-examples that are homeomorphisms was shown in 1943 by Shizuo Kakutani, who...

functional analysis, including the Hahn-Banach and Riesz–Markov–Kakutani representation theorems. Notice also that the neural network is only required to approximate...

Borsuk–Ulam theorem states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point. Here...

value. Glicksberg, I. L. (1952). A Further Generalization of the Kakutani Fixed Point Theorem, with Application to Nash Equilibrium Points. Proceedings of...

traditionally rely on fixed-point theorems such as Brouwer fixed-point theorem for functions (or, more generally, the Kakutani fixed-point theorem for set-valued...

(mathematics) Discontinuous linear map Kakutani fixed-point theorem – Fixed-point theorem for set-valued functions Open mapping theorem (functional analysis) – Condition...

Inner Mongolia University Shizuo Kakutani (角谷 静夫), mathematician, professor at Yale, known for Kakutani fixed-point theorem Ryōji Chūbachi (中鉢良治), a Japanese...

{\displaystyle \operatorname {Wel} } has a fixed-point, we would like to use the Kakutani fixed-point theorem. However, there is a technical issue that...

co-founder of International Economic Review Shizuo Kakutani, mathematician known for Kakutani fixed-point theorem Jun-iti Nagata, topologist Masatoshi Gündüz...