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Existence theorem for a class of generalized quasi-variational inequalities

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  • Monica Milasi

Abstract

In this paper we consider a class of generalized quasi-variational inequalities. The variational problem is studied in the convex set $$X\times Y$$ X × Y , with $$Y$$ Y bounded and $$X$$ X unbounded. In the latter settings, we investigate about the solvability of the problem. In particular, by using the perturbation theory, we give an existence result of the solution without requesting any coercivity hypothesis on the operator. Finally, we give an application to the obtained theoretical results in terms of an economic equilibrium problem. Copyright Springer Science+Business Media New York 2014

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  • Monica Milasi, 2014. "Existence theorem for a class of generalized quasi-variational inequalities," Journal of Global Optimization, Springer, vol. 60(4), pages 679-688, December.
    • Handle: RePEc:spr:jglopt:v:60:y:2014:i:4:p:679-688
    DOI: 10.1007/s10898-013-0114-6
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    References listed on IDEAS

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    1. G. Anello & M. Donato & M. Milasi, 2010. "A quasi-variational approach to a competitive economic equilibrium problem without strong monotonicity assumption," Journal of Global Optimization, Springer, vol. 48(2), pages 279-287, October.
    2. D. Chan & J. S. Pang, 1982. "The Generalized Quasi-Variational Inequality Problem," Mathematics of Operations Research, INFORMS, vol. 7(2), pages 211-222, May.
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    Cited by:

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    2. Sonia & Ratna Dev Sarma, 2023. "A topological approach for vector quasi-variational inequalities with set-valued functions," Computational Management Science, Springer, vol. 20(1), pages 1-13, December.

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