A new approach to the extragradient method for nonlinear variational inequalities
<p/> <p>The approximation-solvability of the following nonlinear variational inequality (NVI) problem is presented:</p> <p>Determine an element <inline-formula><graphic file="1029-242X-2000-158607-i1.gif"/></inline-formula> such that <inline-for...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2000-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/5/158607 |
| _version_ | 1811280505546473472 |
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| author | Verma Ram U |
| author_facet | Verma Ram U |
| author_sort | Verma Ram U |
| collection | DOAJ |
| description | <p/> <p>The approximation-solvability of the following nonlinear variational inequality (NVI) problem is presented:</p> <p>Determine an element <inline-formula><graphic file="1029-242X-2000-158607-i1.gif"/></inline-formula> such that <inline-formula><graphic file="1029-242X-2000-158607-i2.gif"/></inline-formula> where <inline-formula><graphic file="1029-242X-2000-158607-i3.gif"/></inline-formula> is a mapping from a nonempty closed convex subset <inline-formula><graphic file="1029-242X-2000-158607-i4.gif"/></inline-formula> of a real Hilbert space <inline-formula><graphic file="1029-242X-2000-158607-i5.gif"/></inline-formula> into <inline-formula><graphic file="1029-242X-2000-158607-i6.gif"/></inline-formula>. The iterative procedure is characterized as a nonlinear variational inequality (for any arbitrarily chosen initial point <inline-formula><graphic file="1029-242X-2000-158607-i7.gif"/></inline-formula>) <inline-formula><graphic file="1029-242X-2000-158607-i8.gif"/></inline-formula> <inline-formula><graphic file="1029-242X-2000-158607-i9.gif"/></inline-formula> which is equivalent to a double projection formula <inline-formula><graphic file="1029-242X-2000-158607-i10.gif"/></inline-formula> where <inline-formula><graphic file="1029-242X-2000-158607-i11.gif"/></inline-formula> denotes the projection of <inline-formula><graphic file="1029-242X-2000-158607-i12.gif"/></inline-formula> onto <inline-formula><graphic file="1029-242X-2000-158607-i13.gif"/></inline-formula>.</p> |
| first_indexed | 2024-04-13T01:15:59Z |
| format | Article |
| id | doaj.art-d750f82d38f64e849b9d5b4934d19f1d |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-04-13T01:15:59Z |
| publishDate | 2000-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-d750f82d38f64e849b9d5b4934d19f1d2022-12-22T03:08:56ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2000-01-0120004158607A new approach to the extragradient method for nonlinear variational inequalitiesVerma Ram U<p/> <p>The approximation-solvability of the following nonlinear variational inequality (NVI) problem is presented:</p> <p>Determine an element <inline-formula><graphic file="1029-242X-2000-158607-i1.gif"/></inline-formula> such that <inline-formula><graphic file="1029-242X-2000-158607-i2.gif"/></inline-formula> where <inline-formula><graphic file="1029-242X-2000-158607-i3.gif"/></inline-formula> is a mapping from a nonempty closed convex subset <inline-formula><graphic file="1029-242X-2000-158607-i4.gif"/></inline-formula> of a real Hilbert space <inline-formula><graphic file="1029-242X-2000-158607-i5.gif"/></inline-formula> into <inline-formula><graphic file="1029-242X-2000-158607-i6.gif"/></inline-formula>. The iterative procedure is characterized as a nonlinear variational inequality (for any arbitrarily chosen initial point <inline-formula><graphic file="1029-242X-2000-158607-i7.gif"/></inline-formula>) <inline-formula><graphic file="1029-242X-2000-158607-i8.gif"/></inline-formula> <inline-formula><graphic file="1029-242X-2000-158607-i9.gif"/></inline-formula> which is equivalent to a double projection formula <inline-formula><graphic file="1029-242X-2000-158607-i10.gif"/></inline-formula> where <inline-formula><graphic file="1029-242X-2000-158607-i11.gif"/></inline-formula> denotes the projection of <inline-formula><graphic file="1029-242X-2000-158607-i12.gif"/></inline-formula> onto <inline-formula><graphic file="1029-242X-2000-158607-i13.gif"/></inline-formula>.</p>http://www.journalofinequalitiesandapplications.com/content/5/158607Extragradient method<it>g</it>-α-cocoercive mappingDouble projection equationNonlinear quasivariational inequalitiesIterative algorithmsExpanding mappings |
| spellingShingle | Verma Ram U A new approach to the extragradient method for nonlinear variational inequalities Journal of Inequalities and Applications Extragradient method <it>g</it>-α-cocoercive mapping Double projection equation Nonlinear quasivariational inequalities Iterative algorithms Expanding mappings |
| title | A new approach to the extragradient method for nonlinear variational inequalities |
| title_full | A new approach to the extragradient method for nonlinear variational inequalities |
| title_fullStr | A new approach to the extragradient method for nonlinear variational inequalities |
| title_full_unstemmed | A new approach to the extragradient method for nonlinear variational inequalities |
| title_short | A new approach to the extragradient method for nonlinear variational inequalities |
| title_sort | new approach to the extragradient method for nonlinear variational inequalities |
| topic | Extragradient method <it>g</it>-α-cocoercive mapping Double projection equation Nonlinear quasivariational inequalities Iterative algorithms Expanding mappings |
| url | http://www.journalofinequalitiesandapplications.com/content/5/158607 |
| work_keys_str_mv | AT vermaramu anewapproachtotheextragradientmethodfornonlinearvariationalinequalities AT vermaramu newapproachtotheextragradientmethodfornonlinearvariationalinequalities |