Fixed point theorems in \(E\)-\(b\)-metric spaces (Q2926400)
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scientific article; zbMATH DE number 6361259
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fixed point theorems in \(E\)-\(b\)-metric spaces |
scientific article; zbMATH DE number 6361259 |
Statements
24 October 2014
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contraction principle
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fixed point
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iterative method
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multivalued operator
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\(\varphi\)-contraction
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Riesz space
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vector lattice
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vector \(b\)-metric space
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Boyd-Wong contraction
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Fixed point theorems in \(E\)-\(b\)-metric spaces (English)
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Let \((E,\leq)\) be a Riesz space, \(X\) be a nonempty set and \(s\geq1\). The author calls a function \(d:X\times X\to E\) an \(E\)-\(b\)-metric if, for any \(x,y,z\in X\), (a)~\(d(x,y)=0\) if and only if \(x=y\); (b)~\(d(x,y)=d(y,x)\); (c)~\(d(x,z)\leq s[d(x,y)+d(y,z)]\). The triple \((X,d,E)\) is called an \(E\)-\(b\)-space. Boyd-Wong-type fixed point results are proved for single and multivalued mappings in such spaces. No example is given.
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