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

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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).

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Acknowledgements

This work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0024.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Babes-Bolyai University, 1 M. Kogalniceanu, 400084, Cluj-Napoca, Romania

    Gábor Kassay & Mihaela Miholca

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  1. Gábor Kassay
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  2. Mihaela Miholca
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Correspondence to Gábor Kassay.

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Kassay, G., Miholca, M. Existence Results for Variational Inequalities with Surjectivity Consequences Related to Generalized Monotone Operators. J Optim Theory Appl 159, 721–740 (2013). https://doi.org/10.1007/s10957-013-0383-8

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  • DOI: https://doi.org/10.1007/s10957-013-0383-8

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