Existence results for strong vector equilibrium problems and their applications

Abstract

New existence results for the strong vector equilibrium problem are presented, relying on a well-known separation theorem in infinite-dimensional spaces. The main results are applied to strong cone saddle-points and strong vector variational inequalities providing new existence results, and furthermore they allow recovery of an earlier result from the literature.

Keywords:

• equilibrium problems
• existence results
• Henig proper solutions
• strong cone saddle-points
• strong vector variational inequalities

AMS Subject Classifications::

• 49K10
• 90C47

Acknowledgements

The work of the G. Bigi has been supported by the grant PRIN 2007 9PLLN7 ‘Nonlinear Optimization, Variational Inequalities and Equilibrium Problems’ while the work of the A. Capătă by CNCSIS, Grant PN II, ID 523/2007 and the work of the G. Kassay by CNCSIS, Grant PN II, ID 2261, Contract 543/2008.