On the stability for parametric set optimization problems via improvement sets without the strict convexity

In this paper, we aim to discuss the stability of parametric set optimization problems via improvement sets.First, we establish some convergence results for set-valued mappings.Next, under new assumptions, the Berge upper and lower semicontinuity of upper level mappings for parametric set optimization problems with the upper relation are investigated.Then, under suitable assumptions, the sufficient conditions for Berge upper and lower semicontinuity of (weak) minimal solution mappings for parametric set optimization problems via improvement sets are established.