可数族Bregman全局拟-渐进非扩张映射的均衡问题和强收敛定理

Strong convergence theorems for equilibrium problem and countable Bregman totally quasi-asymptotically nonexpansive mappings

摘要:

在实自反的Banach空间中，针对可数族Bregman全局拟-渐进非扩张映射的公共不动点和均衡问题的公共解，构造了一类新型的混合迭代算法，在适当条件下证明了该算法产生的序列的强收敛性．更进一步地，将此方法应用到求解极大单调算子的零点问题上．

Abstract:

In this paper, we propose a new hybrid iterative scheme for finding a common solution of an equilibrium problem and fixed point of countable Bregman totally quasi-asymptotically nonexpansive mappings in reflexive Banach spaces. Moreover, we prove some strong convergence theorems under suitable control conditions. Finally, the application to zero point problem of maximal monotone operators is given by the result.