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Weighted Quasi-Variational Inequalities in Non-pivot Hilbert Spaces and Applications

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Abstract

The paper is devoted to the introduction of weighted quasi-variational inequalities in non-pivot Hilbert spaces. In the first part, we show some existence and regularity results for solutions to such weighted quasi-variational inequalities. The second part concerns the study of a new traffic equilibrium model, where weights and elastic demand occur. A weighted quasi-variational formulation for equilibrium conditions is provided. The general existence and regularity results obtained, in the first part, allow us to show the existence and the continuity of weighted elastic traffic equilibrium solutions. Finally, an example is provided.

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Notes

  1. Where we denote by \(a_{(\alpha_{j})_{k}}\), for k=1,…,d j and j=1,…,l, the kth element of the family α j , for j=1,…,l.

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Authors and Affiliations

  1. Department of Mathematics and Applications, University of Naples ‘Federico II’, via Cintia, 80126, Naples, Italy

    Annamaria Barbagallo

  2. Department of Mathematics and Computer Science, University of Catania, viale Andrea Doria n. 6, 95125, Catania, Italy

    Stéphane Pia

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  1. Annamaria Barbagallo
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  2. Stéphane Pia
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Correspondence to Annamaria Barbagallo.

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Barbagallo, A., Pia, S. Weighted Quasi-Variational Inequalities in Non-pivot Hilbert Spaces and Applications. J Optim Theory Appl 164, 781–803 (2015). https://doi.org/10.1007/s10957-013-0497-z

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