A new approach to the extragradient method for nonlinear variational inequalities

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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Bibliographic Details
Main Author: Verma Ram U
Format: Article
Language:English
Published: SpringerOpen 2000-01-01
Series:Journal of Inequalities and Applications
Subjects:
Extragradient method
<it>g</it>-&#945;-cocoercive mapping
Double projection equation
Nonlinear quasivariational inequalities
Iterative algorithms
Expanding mappings
Online Access:http://www.journalofinequalitiesandapplications.com/content/5/158607
Description
Summary:<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>
ISSN:1025-5834
1029-242X

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