Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-05T03:48:16.422Z Has data issue: false hasContentIssue false
  • English
  • Français

A variational-like inequality problem

Published online by Cambridge University Press:  17 April 2009

J. Parida ,
M. Sahoo  and
A. Kumar
J. Parida
Affiliation:
Department of Mathematics, Regional Engineering College, Rourkela 769008, India
M. Sahoo
Affiliation:
Ispat Vidya Mandir, Rourkela 769005, India
A. Kumar
Affiliation:
Lecturer in Mathematics, Vedvyas College, Rourkela 769041, India
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.

Given a closed and convex set K in Rn and two continuous maps F: K → Rn and η: K × K → Rn, the problem considered here is to find ε K such that

.

We call it a variational-like inequality problem, and develop a theory for the existence of a solution. We also show the relationship between the variational-like inequality problem and some mathematical programming problems.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 2 , April 1989 , pp. 225 - 231
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Ben-Israel, A. and Mond, B., ‘What is invexity’, J. Austral. Math. Soc. 28 (1986), 1–9.CrossRefGoogle Scholar
[2]Berge, C., Topological spaces (Oliver and Boyd, Edinburgh and London, 1963).Google Scholar
[3]Chan, D. and Pang, S., ‘The generalized quasi-variational inequality problem’, Math. Oper. Res. 7 (1982), 211–222.CrossRefGoogle Scholar
[4]Hanson, M.A., ‘On sufficiency of the Kuhn-Tucker Conditions’, J. Math. Anal. Appl. 80 (1981), 545–550.CrossRefGoogle Scholar
[5]Isac, G., ‘On the implicit complementarity problem in Hilbert space’, Bull. Austral. Math. Soc. 32 (1985), 251–260.CrossRefGoogle Scholar
[6]Kakutani, S., ‘A generalization of Brouwer's fixed point theorem’, Duke Math. J. 8 (1941), 457–459.CrossRefGoogle Scholar
[7]Karamardian, S., ‘Generalized complementarity problem’, J. Optim. Theory Appl. 8 (1971), 161–168.CrossRefGoogle Scholar
[8]Kinderlehrer, D. and Stampacchia, G., An introduction to variational inequalities and their applications (Academic Press, New York, 1980).Google Scholar
[9]Mond, B. and Hanson, M.A., ‘On duality with generalized convexity’, Math. Operationsforsch. Statist. Ser. Optim. 15 (1984), 313–317.Google Scholar
[10]More', J.J., ‘Coercivity conditions in nonlinear complementarity problems’, SIAM Rev. 16 (1974), 1–16.CrossRefGoogle Scholar