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 | References | Similar Articles | Additional Information

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

Email:
b-rohani@cc.sbu.ac.ir

**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

Email:
khan@am.uni-erlangen.de, aakhan@mtu.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-03-07000-X

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