Viscosity approximation fixed points for nonexpansive and <inline-formula><graphic file="1687-1812-2006-81325-i1.gif"/></inline-formula>-accretive operators
<p/> <p>Let <inline-formula><graphic file="1687-1812-2006-81325-i2.gif"/></inline-formula> be a real reflexive Banach space, let <inline-formula><graphic file="1687-1812-2006-81325-i3.gif"/></inline-formula> be a closed convex subse...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2006-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2006/81325 |
| Summary: | <p/> <p>Let <inline-formula><graphic file="1687-1812-2006-81325-i2.gif"/></inline-formula> be a real reflexive Banach space, let <inline-formula><graphic file="1687-1812-2006-81325-i3.gif"/></inline-formula> be a closed convex subset of <inline-formula><graphic file="1687-1812-2006-81325-i4.gif"/></inline-formula>, and let <inline-formula><graphic file="1687-1812-2006-81325-i5.gif"/></inline-formula> be an <inline-formula><graphic file="1687-1812-2006-81325-i6.gif"/></inline-formula>-accretive operator with a zero. Consider the iterative method that generates the sequence <inline-formula><graphic file="1687-1812-2006-81325-i7.gif"/></inline-formula> by the algorithm <inline-formula><graphic file="1687-1812-2006-81325-i8.gif"/></inline-formula> where <inline-formula><graphic file="1687-1812-2006-81325-i9.gif"/></inline-formula> and <inline-formula><graphic file="1687-1812-2006-81325-i10.gif"/></inline-formula> are two sequences satisfying certain conditions, <inline-formula><graphic file="1687-1812-2006-81325-i11.gif"/></inline-formula> denotes the resolvent <inline-formula><graphic file="1687-1812-2006-81325-i12.gif"/></inline-formula> for <inline-formula><graphic file="1687-1812-2006-81325-i13.gif"/></inline-formula>, and let <inline-formula><graphic file="1687-1812-2006-81325-i14.gif"/></inline-formula> be a fixed contractive mapping. The strong convergence of the algorithm <inline-formula><graphic file="1687-1812-2006-81325-i15.gif"/></inline-formula> is proved assuming that <inline-formula><graphic file="1687-1812-2006-81325-i16.gif"/></inline-formula> has a weakly continuous duality map.</p> |
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| ISSN: | 1687-1820 1687-1812 |