Upper semicontinuity of the solution maps in homogeneous vector quasi-equilibrium problems

Abstract

The aim of this work was to study the solution maps in the vector homogeneous quasi-equilibrium problems. Here, we establish some sufficient and necessary conditions for upper semicontinuity of the solution maps in the vector homogeneous quasi-equilibrium problems. The results presented extend and improve the preceding results of Oetlli and Yen [Oetlli, W. and Yen, N.D., 1995, Continuity of the solution set of homogeneous equilibrium problems and linear complementarity problems. In: F. Giannessi and A. Maugeri (Eds) Variational Inequalities and Network Equilibrium Problems (New York: Plenum Press)].

Keywords:

• Vector quasi-equilibrium problem
• Solution map
• Homogeneity
• Upper semicontinuity

Keywords:

• Mathematics Subject Classifications 2000: 54C60
• 58C07
• 49J53

Acknowledgment

The authors would like to express their deep thanks to two anonymous referees for their helpful comments and suggestions which led to the improvement of this article.