Abstract
In this paper, we consider vector variational inequalities with set-valued mappings over product sets in a real linear topological space setting. By employing concepts of relative pseudomonotonicity with variable weights, we establish several existence results for generalized vector variational inequalities and for systems of generalized vector variational inequalities. These results strengthen previous existence results which were based on the usual monotonicity type assumptions.
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Allevi, E., Gnudi, A., and Konnov, I.V. (2001), Generalized vector variational inequalities over product sets, Nonlinear Analysis Theory, Methods & Applications, Proceedings of the Third Word Congress of Nonlinear Analysis, Vol. 47, Part 1, Editor-in-chief: V. Lamshmikantham, 573–582.
Ansari, Q.H. and Yao, J.-C. (1999), A fixed point theorem and its applications to a system of variational inequalities, Bull. Austral. Math. Soc., Vol. 59, 433–442.
Ansari, Q.H. and Yao, J.-C., System of generalized variational inequalities and their applications, Applicable Analysis, Vol.76(3–4), 203–217, 2000.
Bianchi, M. (1993), Pseudo P-monotone operators and variational inequalities, Research Report No. 6, Istituto di Econometria e Matematica per le Decisioni Economiche, Università Cattolica del Sacro Cuore, Milan.
Giannessi, F. (1980), Theory of alternative, quadratic programs and complementarity problems, Variational Inequalities and Complementarity Problems, R.W. Cottle, F. Giannessi, and J.L. Lions, eds., Wiley, New York, 151–186.
Hadjisavvas, H. and Schaible, S. (1998), Quasimonotonicity and pseudomo-notonicity in variational inequalities and equilibrium problems, Generalized Convexity, Generalized Monotonicity, J.-P. Crouzeix, J.E. Martinez-Legaz and M. Volle, eds., Kluwer Academic Publishers, Dordrecht — Boston — London, 257–275.
Ky Fan (1961), A generalization of Tychonoff's fixed-point theorem, Math. Annalen, Vol. 142, 305–310.
Konnov, I.V. (1995), Combined relaxation methods for solving vector equilibrium problems, Russ. Math. (Iz. VUZ), Vol. 39, no.12, 51–59.
Konnov, I.V. (2001), Relatively monotone variational inequalities over product sets, Operations Research Letters, Vol. 28, 21–26.
Oettli, W. and Schläger, D. (1998), Generalized vectorial equilibria and generalized monotonicity, Functional Analysis with Current Applications in Science, Technology and Industry, M. Brokate and A.H. Siddiqi, eds., Pitman Research Notes in Mathematical Series, No.377, Addison Wesley Longman Ltd., Essex, 145–154.
Rosen, J.B. (1965), Existence and uniqueness of equilibrium points for concave n-person games, Econometrica, Vol. 33, 520–534.
Yang, X.Q. and Goh, C.J. (1997), On vector variational inequalities: application to vector equilibria, J. Optimiz. Theory and Appl., Vol. 95, 431–443.
Yuan, G.X.Z. (1998), The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities, Memoires of the AMS, Vol.132, Number 625.
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Allevi, E., Gnudi, A., Konnov, I.V. (2005). Decomposable Generalized Vector Variational Inequalities. In: Qi, L., Teo, K., Yang, X. (eds) Optimization and Control with Applications. Applied Optimization, vol 96. Springer, Boston, MA. https://doi.org/10.1007/0-387-24255-4_24
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DOI: https://doi.org/10.1007/0-387-24255-4_24
Publisher Name: Springer, Boston, MA
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