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ON PSEUDOMONOTONE SET-VALUED MAPPINGS IN TOPOLOGICAL VECTOR SPACES

Part of: Existence theories

Published online by Cambridge University Press:  01 October 2008

A. P. FARAJZADEH
A. P. FARAJZADEH*
Affiliation:
Department of Mathematics, Razi University, Kermanshah, 67149, Iran (email: faraj1348@yahoo.com, ali-ff@sci.razi.ac.ir)
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Abstract

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In this paper we extend results of Inoan and Kolumban on pseudomonotone set-valued mappings to topological vector spaces. An application is made to a variational inequality problem.

Keywords

upper semi-continuityC-pseudomonotonicityKnaster–Kuratowski–Mazurkiewicz mapping

MSC classification

Secondary: 49J40: Variational methods including variational inequalities
Type
Research Article
Information
The ANZIAM Journal , Volume 50 , Issue 2 , October 2008 , pp. 258 - 265
Copyright
Copyright © Australian Mathematical Society 2009

References

[1]Blum, E. and Oettli, W., “From optimization and variational inequalities to equilibrium problems”, Math. Stud. 63 (1994) 123–145.Google Scholar
[2]Brezis, H., “Équations et inéquations non lineáires dans les espaces vectoriels en dualité”, Ann. Inst. Fourier (Grenoble) 18 (1968) 115–175.Google Scholar
[3]Fakhar, M. and Zafarani, J., “Generalized vector equilibrium problems for pseudomonotone multivalued bifunctions”, J. Optim. Theory Appl. 126 (2005) 109–124.CrossRefGoogle Scholar
[4]Fan, K., “Some properties of convex sets related to fixed point theorems”, Math. Ann. 266 (1984) 519–537.Google Scholar
[5]Farajzadeh, A. P. and Zafarani, J., Equilibrium problems and variational inequalities in topological vector spaces, Optimization, DOI: 10.1080/02331930801951090, (2008).Google Scholar
[6]Hadjisavvas, N. and Schaible, S., “Generalized monotone maps”, in Handbook of generalized convexity and generalized monotonicity (eds N. Hadjisavvas, S. Komlosi and S. Schaible), (Springer, Berlin, 2005) 389–420.Google Scholar
[7]Inoan, D. and Kolumban, J., “On pseudomonotone set-valued mappings”, Nonlinear Anal. 68 (2008) 47–53.Google Scholar
[8]Karamardian, S., “Complementarity problems over cones with monotone and pseudomonotone maps”, J. Optim. Theory Appl. 18 (1976) 445–454.Google Scholar
[9]Komlosi, S., “Generalized monotonicity in nonsmooth analysis”, in Generalized convexity (eds S. Komlosi, T. Rapcsak and S. Schaible), (Springer, Heidelberg, 1994) 263–275.Google Scholar
[10]Panagiotopoulos, P. D., “Hemivariational inequalities”, in Applications in mechanics and engineering (Springer, Berlin, 1993).Google Scholar
[11]Pshenichnyï, B. N., “Necessary condition for an extremum”, in Pure and applied mathematics, Volume 4 (ed. L. W. Neustade), (Marcel Dekker, New York, 1971) (translated from the Russian by K. Makowski).Google Scholar
[12]Tan, N. T., “Quasi-variational inequalities in topological linear locally convex Hausdorff spaces”, Math. Nachr. 122 (1985) 231–245.Google Scholar
[13]Zhou, J. and Tian, G., “Transfer method for characterizing the existence of maximal elements of binary relations on compact or non compact sets”, SIAM J. Optim. 2 (1992) 360–375.Google Scholar