Banach空间内一类广义混合隐平衡问题组解的存在性和迭代算法  

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

作　　者：丁协平[1] 

机构地区：[1]四川师范大学数学与软件科学学院,成都610068

出　　处：《应用数学和力学》2010年第9期1001-1015,共15页Applied Mathematics and Mechanics

基　　金：四川省重点学科建设基金资助项目(SZD0406);四川师范大学重点科研基金(09ZDL04)对本文的资助

摘　　要：在Banach空间内引入和研究了一类新的广义混合隐平衡问题组.首先,对广义混合隐平衡问题组引入了Yosida逼近映射概念.利用此概念,考虑了一个广义方程问题组并证明了它与广义混合隐平衡问题组的等价性.其次,应用广义方程问题组,建议和分析了计算广义混合隐平衡问题组的近似解的迭代算法.在相当温和的条件下,证明了由算法生成的迭代序列的强收敛性.这些结果是新的并且统一和推广了这一领域内的某些最近结果.A new system of generalized mixed implicity equilibrium problems was introduced and studied in Banach spaces. First, the notion of Yosida proximal mapping for generalized mixed implicity equilibrium problems was introduced. By using the notion, a system of general- ized equation problems was considered and its equivalence with the system of generalized mixed implicity equilibrium problems was also proved. Next, by applying the system of generalized equation problems, an iterative algorithm to compute the approximate solutions of the system of generalized mixed implicity equilibrium problems was suggested and analyzed. The strong convergence of the iterative sequences generated by the algorithm was proved under quite mild conditions. The results are new and unify and generalize some recent results in this field.

关 键 词：广义混合隐平衡问题组 Yosida逼近映射 广义方程问题组 迭代算法 BANACH空间 

分 类 号：O177.91[理学—数学] O241.7[理学—基础数学]