On the solution continuity of parametric set optimization problems (Q328537)

The authors study a parametric set optimization problem with respect to an order relation ``\(\leq^u\)'' introduced by \textit{D. Kuroiwa} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 47, No. 2, 1395--1400 (2001; Zbl 1042.49524)] for sets in a normed space. The main result of the paper states that if the feasible solution set mapping is continuous and has a compact value at a fixed parameter point \(\lambda_0\), the set-valued objective mapping is continuous, has a compact value and if some additional quasi convex hypothesis is satisfied at \(\lambda_0\), then the minimal solution mapping is continuous there.