自反Banach空间内一类新的广义混合平衡问题组的辅助原理和逼近可解性

Auxiliary Principle and Approximation Solvability for a System of New Generalized Mixed Equilibrium 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广义混合平衡问题组(SGMEP).首先,为了求解SGMEP,引入了一类辅助广义混合平衡问题组(SAGMEP).在没有任何强制条件的相当温和假设下,对SAGMEP证明了解的存在性和唯一性.其次,利用辅助原理技巧,对求解SGMEP建议和分析了一类新的迭代算法.最后,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.这些结果改进、统一和推广了这一领域内某些最近结果.

A system of new generalized mixed equilibrium problems involving generalized mixed variational-like inequality problems（SGMEP） was introduced and studied in reflexive Banach spaces.First,a system of auxiliary generalized mixed equilibrium problems（SAGMEP） for solving the SGMEP was introduced.The existence and uniqueness of the solutions of the SAGMEP was proved under quite mild assumptions without any coercive conditions in reflexive Banach spaces.Next,by using the auxiliary principle technique,a new iterative algorithm for solving the SGMEP was suggested and analyzed.Finally,the strong convergence of the iterative sequences generated by the algorithm was also proved under quite mild assumptions without any coercive conditions.These results improve,unify and generalize some recent results in this field.