Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-25T11:12:23.285Z Has data issue: false hasContentIssue false

Some remarks on variational-like and quasivariational-like inequalities

Published online by Cambridge University Press:  17 April 2009

Nguyen Huu Dien
Affiliation:
Institute of Mathematics, P.P. Box 631 Bo Ho 10000 Hanoi, Vietnam
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we study the variational-like inequalities, which generalise some results of Parida, Sahoo and Kumar, and we also investigate the quasivariational-like inequalities. We establish some existence theorems of a solution for the above problem.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Aubin, J.P. and Cellina, A., Differential inclusion (Springer-Verlag, Berlin, Heidelberg, New York, 1984).CrossRefGoogle Scholar
[2]Ben-Israel, A. and Mond, B., ‘What is invexity’, J. Austral. Math. Soc. 28 (1986), 19.CrossRefGoogle Scholar
[3]Bensoussan, A. and Lions, J., Applications des inequations variationelle en controle stochastique (Dunod, Paris, 1978).Google Scholar
[4]Berge, C., Topological spaces (New York, 1963).Google Scholar
[5]Deimling, K., Nonlinear functional analysis (Springer-Verlag, Berlin, Heidelberg, New York, 1985).CrossRefGoogle Scholar
[6]Defigueiredo, D.G., ‘Lectures on the Ekeland variational principle with applications and detours’, Tata Inst. Fund. Res. (1989).Google Scholar
[7]Kinderlehrer, D. and Stampacchia, G., An introduction to variational inequalities and their applications (Academic Press, New York, 1980).Google Scholar
[8]Kuratowski, C., Topologie I (Warsawa, 1950).Google Scholar
[9]Mosco, U., Implicit variational problems and quasivariational inequalities: Lecture Notes in Mathematics 543 (Springer-Verlag, Berlin, Heidelberg, New York, 1976).Google Scholar
[10]Noor, M.A., ‘General variational inequalities’, Appl. Math. Lett. I (1988), 119122.CrossRefGoogle Scholar
[11]Noor, M.A., ‘Iterative algorithms for semilinear quasi complementarity problems’, J. Math. Anal. Appl. 145 (1990), 402412.Google Scholar
[12]Parida, J., Sahoo, M. and Kumar, A., ‘A variation-like inequality problem’, Bull. Austral. Math. Soc. 39 (1989), 225231.CrossRefGoogle Scholar
[13]Smart, D.R., Fixed point theorems, Second edition (Cambridge University Press, 1980).Google Scholar