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1980
In the theory of zero-sum, two-person games the basic theorem was proved by John von Neumann; he used the Brouwer fixed-point theorem. In the theory of many-person games the basic theorem was proved by J. F. Nash; he also used the Brouwer fixed-point theorem. We will prove Nash’s theorem with the Kakutani fixed-point theorem.
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In the theory of zero-sum, two-person games the basic theorem was proved by John von Neumann; he used the Brouwer fixed-point theorem. In the theory of many-person games the basic theorem was proved by J. F. Nash; he also used the Brouwer fixed-point theorem. We will prove Nash’s theorem with the Kakutani fixed-point theorem.
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2018
In Sect. 5.1, we discuss the Banach’s contraction mapping theorem and some consequences of this theorem. We also deal with contractive mappings considered by Edelstein [212] and certain generalizations of contraction mapping theorem, mainly the ones obtained by Boyd and Wongs [75], Kannan [308, 309], Reich [509] and Husain and Sehgal [283] and others ...
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In Sect. 5.1, we discuss the Banach’s contraction mapping theorem and some consequences of this theorem. We also deal with contractive mappings considered by Edelstein [212] and certain generalizations of contraction mapping theorem, mainly the ones obtained by Boyd and Wongs [75], Kannan [308, 309], Reich [509] and Husain and Sehgal [283] and others ...
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On Brouwer's fixed point theorem
Topology Proceedings, 2022Summary: It is shown by Klaas Pieter Hart, Jan van Mill, and Roman Pol [\textit{K. P. Hart} et al., Topol. Proc. 25(Summer), 179--206 (2000; Zbl 1027.54051)] that Brouwer's fixed point theorem can be reduced to its 3-dimensional case by using the hyperspace of a 2-dimensional hereditarily indecomposable continuum.
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A note on the fixed point theorem of Górnicki
Journal of Fixed Point Theory and Applications, 2019R. Bisht
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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
exaly
Experimental quantum key distribution certified by Bell's theorem
Nature, 2022David Nadlinger +2 more
exaly
A common fixed point theorem of Jungck in rectangular b-metric spaces
, 2017Z. Mitrović, S. Radenović
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Orthogonal sets: The axiom of choice and proof of a fixed point theorem
, 2016H. Baghani +2 more
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