Sensitivity for parametric vector equilibria

Abstract

In this article, we consider a parametric vector equilibrium problem in topological vector spaces, or metric spaces, if needed, defined as follows: given , find such that

where the order in Y is defined by a suitable fixed cone C. We study the upper stability of the map of the solutions S=S(λ), providing results in the peculiar framework of generalized monotone functions. In the particular case of a single-valued solution map, we provide conditions for the Hölder regularity of S in both cases when K is fixed, and also when it depends on a parameter.

Keywords:

• Parametric vector equilibrium problems
• Upper hemicontinuity of the solutions
• Vector generalized monotonicity

Keywords:

• Mathematics Subject Classifications 2000: Primary: 47H14
• Secondary: 54C60
• 54C08
• 46A40

Acknowledgment

The authors wish to thank the anonymous referee for the valuable suggestions about the literature on the subject treated.