Abstract: We discussed the Lipschitz continuity for solution mappings of parametric non-convex weak generalized Ky Fan inequality in real normed vector space. Firstly, we gave the concept of a class of nonlinear functional and its basic properties. Secondly, under appropriate assumptions, we established the non-convex separation theorem. Finally, we gave the sufficient theorem of Lipschitz continuity for the solution mappings of parametric non-convex weak generalized Ky Fan inequality under the conditions for the solution mapping without any convexity, monotonicity and univariate, and gave an example to prove the theorem.

Key words:  , Lipschitz continuity, non-convex separation theorem, weak generalized Ky Fan inequality, solution mappings