Banach空间中一类广义混合平衡问题系统解的存在性及算法

Existence and Algorithm of Solutions for a System of Generalized Mixed Equilibrium Problems in Real Banach Spaces

在实Banach空间中引入和研究了一类新的广义混合平衡问题组.首先考虑了一个辅助混合平衡问题组,通过它与广义混合平衡问题组的等价性,证明了它的解的存在性和唯一性;其次构造了广义混合平衡问题组的近似解的迭代算法.在一定的条件下,证明了由算法生成的迭代序列的强收敛性,这些结果推广并改进了近期的某些结果.

A new system of generalized mixed equilibrium problems is studied in Banach spaces.First,a system of auxiliary generalized mixed equilibrium problems is introduced,and its existence and uniqueness are also proved.Next,by applying the system of auxiliary generalized mixed equilibrium problems,an iterative algorithm for solving the system of generalized mixed equilibrium problems is constructed.The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions.These results improve and generalize some recent known results in the literature.