Aim\ [ To study the stability of perturbated set valued functions multiobjective problem in the upper (lower) semi continuous sense. Methods\ Tth theories of topology

convex analysis and functional analysis are used to study and analyze some properties of the set valued function in the problem. Results\ The sufficient conditions of upper semi continuity and lower semi continaity for cone efficient solutions set and weak cone efficient solutions set of the problem are obtained. Conclusion\ The theory of multiobjective programming is complemented.