The Solution by Iteration of Nonlinear Equations in Uniformly Smooth Banach Spaces
LetEbe a uniformly smooth Banach space and letT:D(T)⊂E↦Ebe a strong pseudocontraction with an open domainD(T) inEand a fixed pointx*∈D(T). We establish the strong convergence of the Mann and Ishikawa iterative processes (with errors) to the fixed point ofT. Related results deal with the iterative so...
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| Published in | Journal of mathematical analysis and applications Vol. 215; no. 1; pp. 132 - 146 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
01.11.1997
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| Online Access | Get full text |
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| Summary: | LetEbe a uniformly smooth Banach space and letT:D(T)⊂E↦Ebe a strong pseudocontraction with an open domainD(T) inEand a fixed pointx*∈D(T). We establish the strong convergence of the Mann and Ishikawa iterative processes (with errors) to the fixed point ofT. Related results deal with the iterative solution of operator equations of the formsf∈Txandf∈x+λTx, λ>0, whenTis a set-valued strongly accretative operator. Our theorems include the cases in which the operatorTis defined only locally. Explicit error estimates are also given. |
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| ISSN: | 0022-247X 1096-0813 |
| DOI: | 10.1006/jmaa.1997.5628 |