Hölder continuity results for nonconvex parametric generalized vector quasiequilibrium problems via nonlinear scalarizing functions

Abstract

In this paper, new results for Hölder continuity of the unique solution to a parametric generalized vector quasiequilibrium problem are established via nonlinear scalarization, with and without using the free-disposal condition. Especially, a new kind of monotonicity hypothesis is proposed. The globally Lipschitz property together with other useful properties of the well-known Gerstewitz nonlinear scalarization function are fully exploited for proving. Moreover, our approach does not impose any convexity condition on the considered model. The oriented distance function is also employed for studying Hölder continuity.