Stability of Picard iteration for contractive mappings satisfying an implicit relation (Q2919607)
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scientific article; zbMATH DE number 6090226
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stability of Picard iteration for contractive mappings satisfying an implicit relation |
scientific article; zbMATH DE number 6090226 |
Statements
4 October 2012
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metric space
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fixed point
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Picard iteration
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implicit relation
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error estimate
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rate of convergence
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stability
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almost stability
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summable almost stability
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Stability of Picard iteration for contractive mappings satisfying an implicit relation (English)
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In this paper, the author studies the existence and uniqueness of the fixed point as well as the stability of the Picard iteration for a mapping \(T:X\rightarrow X\) satisfying \(F(d(Tx,Ty),d(x,y),d(x,Tx),d(y,Ty),d(x,Ty),d(y,Tx))\leq 0\), where \((X,d)\) is a complete metric space and \(F:{\mathbb{R}}_+^6\rightarrow{\mathbb{R}}_+\) is a continuous function.
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