A Hybrid Method for Monotone Variational Inequalities Involving Pseudocontractions
<p/> <p>We use strongly pseudocontraction to regularize the following ill-posed monotone variational inequality: finding a point <inline-formula> <graphic file="1687-1812-2011-180534-i1.gif"/></inline-formula> with the property <inline-formula> <graph...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2011-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2011/180534 |
| Summary: | <p/> <p>We use strongly pseudocontraction to regularize the following ill-posed monotone variational inequality: finding a point <inline-formula> <graphic file="1687-1812-2011-180534-i1.gif"/></inline-formula> with the property <inline-formula> <graphic file="1687-1812-2011-180534-i2.gif"/></inline-formula> such that <inline-formula> <graphic file="1687-1812-2011-180534-i3.gif"/></inline-formula>, <inline-formula> <graphic file="1687-1812-2011-180534-i4.gif"/></inline-formula> where <inline-formula> <graphic file="1687-1812-2011-180534-i5.gif"/></inline-formula>, <inline-formula> <graphic file="1687-1812-2011-180534-i6.gif"/></inline-formula> are two pseudocontractive self-mappings of a closed convex subset <inline-formula> <graphic file="1687-1812-2011-180534-i7.gif"/></inline-formula> of a Hilbert space with the set of fixed points <inline-formula> <graphic file="1687-1812-2011-180534-i8.gif"/></inline-formula>. Assume the solution set <inline-formula> <graphic file="1687-1812-2011-180534-i9.gif"/></inline-formula> of (VI) is nonempty. In this paper, we introduce one implicit scheme which can be used to find an element <inline-formula> <graphic file="1687-1812-2011-180534-i10.gif"/></inline-formula>. Our results improve and extend a recent result of (Lu et al. 2009).</p> |
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| ISSN: | 1687-1820 1687-1812 |