Optimality and scalarization of approximate solutions for vector equilibrium problems via Michel-Penot subdifferential

. This paper is devoted to the investigation of the optimality and scalarization for approximate solutions to a Constrained Vector Equilibrium Problem (CVEP). The optimality conditions are given in terms of Michel-Penot subdifferentials, and the scalarization theorems are proposed via a strongly monotone cone convex function. We firstly establish a necessary condition for an approximate quasi weakly efficient solution to problem (CVEP). Then, a sufficient condition for approximate quasi Benson proper efficient solutions to problem (CVEP) is examined under the newly introduced generalized convexity assumptions. Finally, by using the properties of Bishop-Phelps cone, we present the scalarization theorems for approximate quasi weakly (Benson proper) efficient solutions.