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Vector equilibrium problems on unbounded sets

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Abstract

We consider a general vector equilibrium problem in a reflexive Banach space setting and propose a new coercivity condition for the case of unbounded sets. This condition enables us to obtain new existence results of solutions for vector equilibrium problems. We specialize these results for scalar equilibrium problems and vector variational inequalities.

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Authors and Affiliations

  1. Department of System Analysis and Information Technologies, Kazan University, ul. Kremlevskaya, 18, Kazan, 420008, Russia

    I. V. Konnov

  2. Faculty of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, Guangxi, 530006, P.R. China

    Z. Liu

Authors
  1. I. V. Konnov
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  2. Z. Liu
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Corresponding author

Correspondence to I. V. Konnov.

Additional information

Submitted by O.E. Tikhonov

This work was supported by the joint RFBR-NNSF grant, project No. 07-01-92101 and by the NNSF grant No. 10971019.

The second author was also supported by the Guangxi NSF grant No. 2010GXNSFA013114.

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Konnov, I.V., Liu, Z. Vector equilibrium problems on unbounded sets. Lobachevskii J Math 31, 232–238 (2010). https://doi.org/10.1134/S1995080210030066

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  • DOI: https://doi.org/10.1134/S1995080210030066

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