Banach空间内广义混合隐平衡问题组的可解性(英文)

Approximation Solvability of System of Generalized Mixed ImplicitEquilibrium Problems in Banach Spaces

在Banach空间内引入和研究了一类新的涉及非单调集值映像的广义混合隐平衡问题组.首先推广了由Moudafi在Hilbert空间内引入的Yosida逼近概念到自反Banach空间.利用这一Yosida逼近概念,考虑了一个广义Wiener-Hopf方程问题组并且证明了它与此广义混合隐平衡问题组是等价的.由使用广义Wiener-Hopf方程问题组的不动点陈述,建议和分析了求解广义混合隐平衡问题组的一类新的迭代算法.在适当条件下,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某些最近结果.

A new system of generalized mixed implicit equilibrium problems involving non-monotone set-valued mappings is introduced and studied in real Banach spaces.The notion of the Yosida approximation introduced by Moudafi in Hilbert spaces is first generalized to reflexive Banach spaces.Further,by using the notion of the Yosida approximation,a system of generalized Wiener-Hopf equations problems is considered and its equivalence with the system of generalized mixed implicit equilibrium problems is also proved.By using a fixed point formulation of the system of generalized Wiener-Hopf equations problems,a new iterative algorithm for solving the system of generalized mixed implicit equilibrium problems is suggested and analyzed.The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions.These results are new and unify and generalize some recent results in this field.