Lipschitz Continuity of Approximate Solution Mappings to Parametric Generalized Vector Equilibrium Problems

Abstract

In this paper, we establish Lipschitz continuity of strongly efficient approximate solution mapping to parametric generalized vector equilibrium problems without using monotonicity and any information of the solution mappings. Moreover, we make a new attempt to establish Lipschitz continuity of weakly efficient approximate solution mapping and efficient approximate solution mapping to parametric generalized vector equilibrium problems by using a scalarization method and a density result, respectively. As an application of the main results, we obtain Lipschitz continuity of strongly efficient approximate solution mapping, weakly efficient approximate solution mapping and efficient approximate solution mapping to parametric vector optimization problems.