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Existence Results for Variational Inequalities with Surjectivity Consequences Related to Generalized Monotone Operators

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  • Gábor Kassay

    (Babes-Bolyai University)

  • Mihaela Miholca

    (Babes-Bolyai University)

Abstract

We present existence results for variational inequalities given by generalized monotone operators. As a consequence, we deduce the existence of zeros, or even more, the surjectivity of some classes of set-valued operators. We show that by strengthening the continuity assumptions, similar surjectivity results can be obtained without any monotonicity assumption. In the framework of reflexive Banach spaces, we extend a related result due to Inoan and Kolumbán (Nonlinear Anal. 68:47–53, 2008).

Suggested Citation

  • Gábor Kassay & Mihaela Miholca, 2013. "Existence Results for Variational Inequalities with Surjectivity Consequences Related to Generalized Monotone Operators," Journal of Optimization Theory and Applications, Springer, vol. 159(3), pages 721-740, December.
    • Handle: RePEc:spr:joptap:v:159:y:2013:i:3:d:10.1007_s10957-013-0383-8
    DOI: 10.1007/s10957-013-0383-8
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    References listed on IDEAS

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    1. M. Bianchi & R. Pini, 2005. "Coercivity Conditions for Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 124(1), pages 79-92, January.
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