Robustness of Mann Type Algorithm with Perturbed Mapping for Nonexpansive Mappings in Banach Spaces
<p/> <p>The purpose of this paper is to study the robustness of Mann type algorithm in the sense that approximately perturbed mapping does not alter the convergence of Mann type algorithm. It is proven that Mann type algorithm with perturbed mapping <inline-formula> <graphic fil...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2010/734181 |
| Summary: | <p/> <p>The purpose of this paper is to study the robustness of Mann type algorithm in the sense that approximately perturbed mapping does not alter the convergence of Mann type algorithm. It is proven that Mann type algorithm with perturbed mapping <inline-formula> <graphic file="1687-1812-2010-734181-i1.gif"/></inline-formula> remains convergent in a Banach space setting where <inline-formula> <graphic file="1687-1812-2010-734181-i2.gif"/></inline-formula>, <inline-formula> <graphic file="1687-1812-2010-734181-i3.gif"/></inline-formula> a nonexpansive mapping, <inline-formula> <graphic file="1687-1812-2010-734181-i4.gif"/></inline-formula>, <inline-formula> <graphic file="1687-1812-2010-734181-i5.gif"/></inline-formula>, errors and <inline-formula> <graphic file="1687-1812-2010-734181-i6.gif"/></inline-formula> a strongly accretive and strictly pseudocontractive mapping.</p> |
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| ISSN: | 1687-1820 1687-1812 |