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1998
We begin by the well-known Banach contraction principle. A mapping f: X → Y from a metric space (X, ρ ) into a metric space (Y, d) is said to be a contraction if there is a number 0 ≤ γ < 1 such that inequality \( d\left( {f\left( x \right),f\left( {x'} \right)} \right) \leqslant \gamma \cdot \rho \left( {x,x'} \right) \) holds, for every pair of ...
Dušan Repovš +1 more
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We begin by the well-known Banach contraction principle. A mapping f: X → Y from a metric space (X, ρ ) into a metric space (Y, d) is said to be a contraction if there is a number 0 ≤ γ < 1 such that inequality \( d\left( {f\left( x \right),f\left( {x'} \right)} \right) \leqslant \gamma \cdot \rho \left( {x,x'} \right) \) holds, for every pair of ...
Dušan Repovš +1 more
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A contractive type fixed point theorem for a mapping \(f: X\times X\to X\), \(X\) a compact metric space, is proved.
Bhola, P. K., Sharma, P. L.
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Bhola, P. K., Sharma, P. L.
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Generalisation of a fixed point theorem
1985The following fixed point theorem has been proved in [\textit{J. Achari} and \textit{B. K. Lahiri}, Riv. Mat. Univ. Parma, IV. Ser. 6, 161-165 (1980; Zbl 0463.47038)]. Theorem: Let \(X\) be a reflexive Banach space and \(K\) be a non-empty closed convex bounded subset of \(X\).
Tiwary, Kalishankar, Lahiri, B. K.
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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
Orthogonal sets: The axiom of choice and proof of a fixed point theorem
, 2016H. Baghani +2 more
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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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A common fixed point theorem of Jungck in rectangular b-metric spaces
, 2017Z. Mitrović, S. Radenović
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Random fixed point theorem in generalized Banach space and applications
, 2016Moulay Larbi Sinacer +2 more
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