Prederivatives of gamma paraconvex set-valued maps and Pareto optimality conditions for set optimization problems

摘要

Prederivatives play an important role in the research of set optimization problems. First, we establish several existence theorems of prederivatives for γ-paraconvex set-valued mappings in Banach spaces with γ 0 $gamma0$ . Then, in terms of prederivatives, we establish both necessary and sufficient conditions for the existence of Pareto minimal solution of set optimization problems.