Well-posedness And Stability Of Vector Equilibrium Problems

In this paper, the research background of well-posedness and stability of vectorequilibrium problems is introduced in the first chapter. In the second chapter, it gavethe relevant basic knowledge.In the third chapter, concept of generalized Levitin-Polyak well-posedness ofsymmetric strong vector quasi-equilibrium problem is introduced. Thecharacterizations for generalized Levitin-Polyak well-posedness of the symmetricstrong vector quasi-equilibrium problem and the symmetric weak vectorquasi-equilibrium problem are given by closed graph of the approximating solutionmapping.In the fourth chapter, the lower semicontinuity of solution mapping to parametricgeneralized strong vector equilibrium problems without the assumptions ofmonotonicity and compactness is established by using a new proof method which isdifferent from the ones used in the literature.In the fifth chapter, by ensuring the existence of solutions, H(?)lder continuity ofapproximate solutions to parametric strong vector equilibrium problems with respectto Hausdorff metric is established.