自反Banach空间内涉及广义混合似变分不等式问题的双水平广义混合平衡问题

Bilevel Generalized Mixed Equilibrium Problems Involving Generalized Mixed Variational-Like Inequality Problems in Reflexive Banach Spaces

在自反Banach空间内,引入和研究了一类新的涉及广义混合似变分不等式问题的双水平广义混合平衡问题(BGMEP).首先,为了计算BGMEP的近似解,引入了一类辅助广义混合平衡问题(AGMEP).由使用一极小极大不等式,在没有任何强制条件的相当温和假设下,证明了AGMEP解的存在性和唯一性.利用辅助原理技巧,建议和分析了一类计算BGMEP的近似解的新迭代算法.在没有任何强制条件的相当温和假设下,证明了由算法生成的迭代序列的强收敛性.这些结果是新的并且推广了这一领域内某些最近结果.

A new class of bilevel generalized mixed equilibrium problems （BGMEP） involving generalized mixed variational-like inequality problems was introduced and studied in reflexive Banach spaces. First, an auxiliary generalized mixed equilibrium problem （AGMEP） to compute the approximate solutions of the bilevel generalized mixed equilibrium problems involving generalized mixed variational-like inequality problems was introduced. By using a minimax inequality, the existence and uniqueness of solutions of the AGMEP was proved under quite mild conditions without any coercive assumptions. By using auxiliary principle technique, new iteratire algorithm to compute the approximate solutions of the BGMEP were suggested and analyzed. The strong convergence of the iterative sequences generated by the algorithms was proved under quite mild conditions without any coercive assumptions. These results are new and generalize some recent results in this field.