Gap Functions and Existence of Solutions for a System of Vector Equilibrium Problems

  • N. J. Huang
  • J. Li
  • J. C. YaoEmail author


In this paper, a gap function for a system of vector equilibrium problems is introduced and studied. Some necessary and sufficient conditions for the system of vector equilibrium problems are established. Characterizations of the solutions set for the system of vector equilibrium problems are also derived. Furthermore, some existence results of solutions for the system of vector equilibrium problems are proved.


Systems of vector equilibrium problems Gap functions Convex cones Point-to-set mappings 


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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of MathematicsSichuan UniversityChengduPeople’s Republic of China
  2. 2.Department of MathematicsChina West Normal UniversityNanchongPeople’s Republic of China
  3. 3.Department of Applied MathematicsNational Sun Yat-Sen UniversityKaohsiungTaiwan

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