On the embedding of variational inequalities
Authors:
B. Djafari Rouhani and A. A. Khan
Journal:
Proc. Amer. Math. Soc. 131 (2003), 38613871
MSC (2000):
Primary 47A52; Secondary 47H14
Published electronically:
May 8, 2003
MathSciNet review:
1999935
Fulltext PDF Free Access
Abstract 
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Abstract: This work is devoted to the approximation of variational inequalities with pseudomonotone 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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 F. E. Browder and B. A. Ton: Nonlinear functional equations in Banach spaces and elliptic super regularization, Math. Zeitschr., Vol. 105, pp. 177195 (1968). MR 38:582
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 F. Giannessi: Embedding variational inequalities and their generalizations into a separation scheme, J. Inequal. Appl. 1, pp. 139147 (1997). MR 2000j:49017
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 J. Gwinner: A note on pseudomonotone functions, regularization, and relaxed coerciveness, Nonlinear Analysis, Vol. 30, pp. 42174227 (1997).
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 A. A. Khan: A regularization approach for variational inequalities, Comput. Math. Appl., Vol. 42, pp. 6574 (2001). MR 2002b:49020
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 D. Kinderlehrer and G. Stampacchia: An introduction to variational inequalities and their applications, Academic Press, New York, 1980. MR 81g:49013
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 U. Mosco: Convergence of convex sets and of solutions of variational inequalities, Adv. Math. Vol. 3, pp. 510585 (1969). MR 45:7560
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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 193954716 Evin, 19834 Tehran, Iran
Email:
brohani@cc.sbu.ac.ir
A. A. Khan
Affiliation:
Institute of Applied Mathematics, University of ErlangenNürnberg, 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 499311295
Email:
khan@am.unierlangen.de, aakhan@mtu.edu
DOI:
http://dx.doi.org/10.1090/S000299390307000X
PII:
S 00029939(03)07000X
Keywords:
Variational inequalities,
regularization,
pseudomonotone,
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
