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On the Kakutani fixed point theorem and its relationship with the selection problem I
Surendra-Nath Patnaik
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Kakutani-type fixed point theorems: A survey
The contents of this paper is best described by quoting its summary: ``A Kakutani-type fixed point theorem refers to a theorem of the following kind: Given a group or semigroup \(S\) of continuous affine transformations \(s:Q\rightarrow Q\), where \(Q\) is a nonempty compact convex subset of a Hausdorff locally convex linear topological space, then ...
I. Namioka
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Conditions for the Uniqueness of the Fixed Point in Kakutani's Theorem
Canadian Mathematical Bulletin, 1981AbstractKakutani's Theorem states that every point convex and use multifunction ϕ defined on a compact and convex set in a Euclidean space has at least one fixed point. Some necessary conditions are given here which ϕ must satisfy if c is the unique fixed point of ϕ. It is e.g.
H. Schirmer
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On Kakutani's fixed point theorem, the K-K-M-S theorem and the core of a balanced game
Economic Theory, 1991zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shapley, Lloyd, Vohra, Rajiv
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A new form of Kakutani fixed point theorem and intersection theorem with applications
2021In this paper sufficient conditions for the existence of a solution for the inclusion problem \(x^*\in \operatorname{conv}(A(x^*))\) are given. Some consequences are obtained. Unfortunately, the paper contains some typos/misprints that make it difficult to understand.
Farajzadeh, Ali P. +2 more
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Inverse Maximum Theorems and Their Relations with Equilibrium and Fixed Point Theorems
Journal of Optimization Theory and Applications, 2023J. Cotrina, Raúl Fierro
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History of the Brouwer Fixed Point Theorem
Progress in Nonlinear Differential Equations and Their Applications, 2020G. Dincă, J. Mawhin
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Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
Nature Machine Intelligence, 2021Lu Lu, Pengzhan Jin, Guofei Pang
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Experimental quantum key distribution certified by Bell's theorem
Nature, 2022David Nadlinger +2 more
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