Banach空间内新的参数广义混合隐平衡问题组的灵敏性分析(英文)

Sensitivity Analysis for a New System of Parametric Generalized Mixed Implicity Equilibrium Problems in Banach Spaces

在实Banach空间内引入和研究了一类新的涉及非单调集值映射的参数广义混合隐平衡问题组(SPGMIEP).首先,引入了一个辅助混合平衡问题(AMEP).在没有任何强制条件的相当温和的假设下对AMEP证明了解的存在唯一性.其次,由使用AMEP的解映射引入了一个参数广义方程问题组(SPGEP)和证明了它与SPGMIEP的等价性.由使用SPGEP的不动点陈述,研究了SPGMIEP的解集的行为和灵敏性分析.在适当假设下证明了SPGMIEP的解集是非空闭的并且关于参数是Lipschitz连续的.这些结果是新的并且改进和推广了该领域的某些已知结果.

In this paper, a new system of parametric generalized mixed implicity equilibrium problems （SPG- MIEP） involving non-monotone set-valued mappings is introduced and studied in real Banach spaces. First, an auxiliary mixed equilibrium problem （AMEP） is introduced. The existence and uniqueness of solutions of the AMEP is proved under quite mild assumptions without any coercive conditions. Next, by using the solution map- ping of the AMEP, a system of parametric generalized equation problems （SPGEP） is considered and its equiva- lence with the SPGMIEP is also proved. By using a fixed point formulation of the SPGEP, we study the behavior and sensitivity analysis of solution set of the SPGMIEP. Under suitable assumptions, we prove that the solution set of the SPGMIEP is nonempty, closed and Lipsehitz continuous with respect to the parameters. Our results are new, which improve and generalize some known results in this field.