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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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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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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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1994
The following fixed point theorem in a complete metric space is proved: Let \((X,d)\) be a bounded complete metric space and let \(T\) be a continuous mapping of \(X\) into itself. Let \(\varphi: \mathbb{R}_+^5\to \mathbb{R}_+\) be nondecreasing in each variable and let \(T\) satisfy the following condition for \(x\neq y\): \[ d(Tx,Ty)< \varphi\{d(x,Tx)
Tiwary, Kalishankar, Singh, G. N.
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The following fixed point theorem in a complete metric space is proved: Let \((X,d)\) be a bounded complete metric space and let \(T\) be a continuous mapping of \(X\) into itself. Let \(\varphi: \mathbb{R}_+^5\to \mathbb{R}_+\) be nondecreasing in each variable and let \(T\) satisfy the following condition for \(x\neq y\): \[ d(Tx,Ty)< \varphi\{d(x,Tx)
Tiwary, Kalishankar, Singh, G. N.
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