Well-posedness For Strong Vector Equilibrium Problems And Connectedness Of Solution Set For The Weak Vector Equilibrium Problems

The paper studied well-posedness for strong vector equilibrium problems in normed spaces in the third chapter. Under suitable conditions, it derived necessary and sufficient conditions to the unique well-posedness and well-posedness. Then we discussed the sufficient conditions to the unique well-posedness and well-posedness, when the mapping satisfied some different conditions in the two arguments. Finally, it discussed the relationship of well-posedness for between vector equilibrium problems and optimization problem and derived the equivalent condition between well-posedness for vector equilibrium problems and well-posedness for optimization problem.In the fourth chapter, it discussed the connectedness of weak efficiency set for vector equilibrium with a mapping which is the sum of two functions with different conditions, in real locally convex Hausdorff topological vector spaces, under some suitable assumptions. Fist, it studied the existence of the f-efficiency through C-monotone and convex of the functions. Then it composed a set-valued mapping which is upper semicontinuous. Finally, it proved the weak efficiency solution is connected through the concave of the functions.