ON GENERALIZED VECTOR QUASI EQUILIBRIUM INEQUALITY PROBLEM VIA SCALARIZATION - Zangenehmehr, P.; Farajzadeh, A.P.; Karamian, AR. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2015)
In this note, we consider the nonlinear scalarization function in topological vector spaces and present some properties of it and by using the nonlinear scalarization function we establish an existence theorem for a solution of a generalized quasi-vector equilibrium problem. Moreover, we show that under suitable conditions the solution set of the generalized quasi-vector equilibrium problem is compact.