Stability on parametric strong symmetric quasi-equilibrium problems via nonlinear scalarization

Abstract

. This paper focuses on the stability analysis of a class of parametric strong symmetric quasiequilibrium problems (PSSQEP) via scalarization approaches. Based on the oriented distance function, a new nonlinear scalarization function which can separate sets { 0 } and − C \{ 0 } is presented. By virtue of the scalarization function, a new form of scalar parametric strong symmetric quasi-equilibrium problem (PSSQEP) ψ is obtained, and the union relation between the solution set of (PSSQEP) and the solution sets of a series of (PSSQEP) ψ is established. Finally, the sufficient conditions of the Berge-semicontinuity of solution mappings for (PSSQEP) are obtained via the union relation and the nonlinear scalarization technique, which is different from the scalarization method recently announced. Some interesting examples are given to illustrate the main results.