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On the embedding of variational inequalities

Authors: B. Djafari Rouhani and A. A. Khan
Journal: Proc. Amer. Math. Soc. 131 (2003), 3861-3871
MSC (2000): Primary 47A52; Secondary 47H14
Published electronically: May 8, 2003
MathSciNet review: 1999935
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Abstract: This work is devoted to the approximation of variational inequalities with pseudo-monotone operators. A variational inequality, considered in an arbitrary real Banach space, is first embedded into a reflexive Banach space by means of linear continuous mappings. Then a strongly convergent approximation procedure is designed by regularizing the embedded variational inequality. Some special cases have also been discussed.

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Additional Information

B. Djafari Rouhani
Affiliation: Institute for Studies in Nonlinear Analysis, School of Mathematical Sciences, Shahid Beheshti University, P.O. Box 19395-4716 Evin, 19834 Tehran, Iran

A. A. Khan
Affiliation: Institute of Applied Mathematics, University of Erlangen-Nürnberg, Martensstr. 3, 91058 Erlangen, Germany
Address at time of publication: Department of Mathematical Sciences, Michigan Technological University, 319 Fisher Hall, 1400 Townsend Drive, Houghton, Michigan 49931-1295

Keywords: Variational inequalities, regularization, pseudo-monotone, embedding
Received by editor(s): October 22, 2001
Received by editor(s) in revised form: August 1, 2002
Published electronically: May 8, 2003
Additional Notes: The first author’s research was supported by a grant from Shahid Beheshti University
The second author’s research was supported by the German Science Foundation (DFG)
Dedicated: Dedicated to Jochem Zowe on the occasion of his sixtieth birthday
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society