Results 321 to 330 of about 416,861 (348)
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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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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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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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A Remark on the Caristi’s Fixed Point Theorem and the Brouwer Fixed Point Theorem
2020It is well-known that a partial order induced from a lower semi-continuous map gives us a clear picture of a proof of the Caristi’s fixed point theorem. The proof utilized Zorn’s lemma to guarantee the existence of a minimal element which turns out to be a desired fixed point.
P. Kumam, S. Dhompongsa
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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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Some generalizations of fixed point theorems and common fixed point theorems
Journal of Fixed Point Theory and Applications, 2018We present some fixed point theorems and common fixed point theorems which generalize and unify previous known results.
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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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Functional Analysis and Its Applications, 1996
Tran Quoc Binh, Nguyen Minh Chuong
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Tran Quoc Binh, Nguyen Minh Chuong
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