More on the behaviors of fixed points sets of multifunctions and applications

Abstract

In this paper, we study the behaviors of fixed points sets of non necessarily pseudo-contractive multifunctions. Rather than comparing the images of the involved multifunctions, we make use of some conditions on the fixed points sets to establish general results on their stability and continuous dependence. We illustrate our results by applications to differential inclusions and give stability results of fixed points sets of non necessarily pseudo-contractive multifunctions with respect to the bounded proximal convergence.

Keywords

• multifunction
• fixed point
• Pompeiu-Hausdorff metric
• bounded proximal convergence
• differential inclusion