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The Ran–Reurings fixed point theorem without partial order: A simple proof
, 2014The purpose of this note is to generalize the celebrated Ran–Reurings fixed point theorem to the setting of a space with a binary relation that is only transitive (and not necessarily a partial order) and a relation-complete metric.
H. Ben-el-Mechaiekh
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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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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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Some generalizations of fixed point theorems and common fixed point theorems
Journal of Fixed Point Theory and Applications, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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, Pavel V. Semenov
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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, Pavel V. Semenov
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A fixed point theorem for self-maps of a complete metric space fulfilling a contractive type condition is presented.
Bhola, Praveen K., Sharma, P. L.
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Bhola, Praveen K., Sharma, P. L.
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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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Orthogonal sets: The axiom of choice and proof of a fixed point theorem
, 2016H. Baghani +2 more
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