S-derivative of perturbed mapping and solution mapping for parametric vector equilibrium problems

Abstract

Abstract In this paper, we deal with the sensitivity analysis in vector equilibrium problems by using the S-derivative of a set-valued mapping. We first investigate the S-derivative on a kind of set-valued gap function for the vector equilibrium problems. Based on these results, S-derivative estimations on a perturbed mapping for the parametric vector equilibrium problem are given. Moreover, we provide some examples to illustrate the obtained results. Finally, we derive the S-derivative estimations of a solutions mapping of the parametric vector equilibrium problems via S-derivative estimations of a kind of the parametric variational system.

Keywords

• Parametric vector equilibrium problems
• Set-valued gap function
• Perturbed mapping
• Solution mapping
• S-derivative
• Sensitivity analysis