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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.
J. Franklin
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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.
J. Franklin
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The Annals of Mathematics, 1951
where f, p are continuous, g satisfies a Lipschitz condition, p(t) has period 1, and g(t)/I ? 1 for large t at any rate. Our choice of hypotheses and the main lines of our investigations have been dominated by what is significant in the theory of differential equations, but our results are concerned solely with sets of points and transformations of ...
Cartwright, M. L., Littlewood, J. E.
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where f, p are continuous, g satisfies a Lipschitz condition, p(t) has period 1, and g(t)/I ? 1 for large t at any rate. Our choice of hypotheses and the main lines of our investigations have been dominated by what is significant in the theory of differential equations, but our results are concerned solely with sets of points and transformations of ...
Cartwright, M. L., Littlewood, J. E.
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2008
This article gives statements of the Tarski fixed point theorem and the main versions of the topological fixed point principle that have been ...
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This article gives statements of the Tarski fixed point theorem and the main versions of the topological fixed point principle that have been ...
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Subrahmanyam’s fixed point theorem
Nonlinear Analysis: Theory, Methods & Applications, 2009In this paper, a sufficient and necessary condition for the convergence of the sequence of successive \(\{T^n x\}\) approximations to a fixed point of self mapping \(T\) on a complete metric space \((X, d)\) is given. Some equivalent conditions for the convergence of the sequence of successive \(\{T^n x\}\) approximations to a unique fixed point of ...
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New fixed point theorems for set-valued contractions in b-metric spaces
, 2015In this paper, we indicate a way to generalize a series of fixed point results in the framework of b-metric spaces and we exemplify it by extending Nadler’s contraction principle for set-valued functions (see Nadler, Pac J Math 30:475–488, 1969) and a ...
R. Miculescu, A. Mihail
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1987
An economic system, which consists of a number of relationships among the relevant factors, is modelled as a system of equations or inequalities of certain unknowns, whose solution represents a specific state in which the system settles. This is typically exemplified by the Walrasian competitive economy (Walras, 1874), consisting of the interaction of ...
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An economic system, which consists of a number of relationships among the relevant factors, is modelled as a system of equations or inequalities of certain unknowns, whose solution represents a specific state in which the system settles. This is typically exemplified by the Walrasian competitive economy (Walras, 1874), consisting of the interaction of ...
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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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Heterogeneous Vectorial Fixed Point Theorems
Mediterranean Journal of Mathematics, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tiziana Cardinali +2 more
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