The new fastest hybrid iteration process (Q2923282)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: The new fastest hybrid iteration process |
scientific article; zbMATH DE number 6356014
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The new fastest hybrid iteration process |
scientific article; zbMATH DE number 6356014 |
Statements
15 October 2014
0 references
\(K\)-normed linear space
0 references
fixed point
0 references
Picard iteration
0 references
Picard-Mann iteration
0 references
convergence order
0 references
The new fastest hybrid iteration process (English)
0 references
In order to approximate the unique fixed point (presumed to exist) of a mapping \(T: X\rightarrow X\) satisfying the contraction condition NEWLINE\[NEWLINE |Tx-Ty|\leq \delta |x-y|+\Phi (|x-Tx|) \text{ for all } x, y\in X NEWLINE\]NEWLINE in a \(K\)-normed linear space \(X\), the author uses the Picard iteration of the iterate \(T^2\) and shows that this method converges faster than the Picard-Mann iteration with respect to the convergence order introduced by the reviewer in [Fixed Point Theory Appl. 2004, No. 2, 97--105 (2004; Zbl 1090.47053)].
0 references
0.8161534070968628
0 references
0.793657124042511
0 references
