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Erschienen in:
2011 | OriginalPaper | Buchkapitel
The Generalized Mann Iterative Process with Errors for Strongly Pseudocontractive Mappings in Arbitrary Banach Spaces
verfasst von : Cheng Wang, Hai-E Zhang, Zhi-Ming Wang
Erschienen in: Information Computing and Applications
Verlag: Springer Berlin Heidelberg
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Let
E
be a real Banach space and
D
be a nonempty closed convex subset of
E
. Suppose that
T
:
D
→
D
is a uniformly continuous and strongly pseudocontractive mapping with bounded range. It is proved that the generalized Mann iterative process with errors converges strongly to the unique fixed point of
T
. It is also to establish the convergence theorems of the new iterative methods for strongly pseudocontractive and strongly accretive operators in Banach spaces. The related results deal with the approximation of the solutions of nonlinear equation for strongly accretive operators.