Weak Convergence Theorems of Three Iterative Methods for Strictly Pseudocontractive Mappings of Browder-Petryshyn Type
<p>Abstract</p> <p>Let <inline-formula> <graphic file="1687-1812-2008-672301-i1.gif"/></inline-formula> be a real <inline-formula> <graphic file="1687-1812-2008-672301-i2.gif"/></inline-formula>-uniformly smooth Banach space w...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2008-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2008/672301 |
| Summary: | <p>Abstract</p> <p>Let <inline-formula> <graphic file="1687-1812-2008-672301-i1.gif"/></inline-formula> be a real <inline-formula> <graphic file="1687-1812-2008-672301-i2.gif"/></inline-formula>-uniformly smooth Banach space which is also uniformly convex (e.g., <inline-formula> <graphic file="1687-1812-2008-672301-i3.gif"/></inline-formula> or <inline-formula> <graphic file="1687-1812-2008-672301-i4.gif"/></inline-formula> spaces <inline-formula> <graphic file="1687-1812-2008-672301-i5.gif"/></inline-formula>, and <inline-formula> <graphic file="1687-1812-2008-672301-i6.gif"/></inline-formula> a nonempty closed convex subset of <inline-formula> <graphic file="1687-1812-2008-672301-i7.gif"/></inline-formula>. By constructing nonexpansive mappings, we elicit the weak convergence of Mann's algorithm for a <inline-formula> <graphic file="1687-1812-2008-672301-i8.gif"/></inline-formula>-strictly pseudocontractive mapping of Browder-Petryshyn type on <inline-formula> <graphic file="1687-1812-2008-672301-i9.gif"/></inline-formula> in condition thet the control sequence <inline-formula> <graphic file="1687-1812-2008-672301-i10.gif"/></inline-formula> is chosen so that (i) <inline-formula> <graphic file="1687-1812-2008-672301-i11.gif"/></inline-formula> (ii) <inline-formula> <graphic file="1687-1812-2008-672301-i12.gif"/></inline-formula>, where <inline-formula> <graphic file="1687-1812-2008-672301-i13.gif"/></inline-formula>. Moreover, we consider to find a common fixed point of a finite family of strictly pseudocontractive mappings and consider the parallel and cyclic algorithms for solving this problem. We will prove the weak convergence of these algorithms.</p> |
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| ISSN: | 1687-1820 1687-1812 |