Bregman广义弱相对非扩张与均衡问题的强收敛定理及其应用

Strong convergence theorems and its applications for equilibrium problems and Bregman generalized weak relatively nonexpansive mapping

在自反的Banach空间中,引入Bregman广义弱相对非扩张映射概念,针对均衡问题和Bregman广义弱相对非扩张映射的不动点问题的公共解,构造了一种新的迭代算法,并在适当的条件下得到了该算法的强收性.最后,将本文结论应用在极大单调算子的零点问题上.

In this paper,we introduce a concept of generalized weak relatively nonexpansive mapping and construct a new algorithms for finding a common solution to equilibrium problem and fixed point of the mapping that generalize the concept of nonexpansivity in reflexive real Banach spaces.Moreover,the strong convergence of the proposed algorithms is proved under appropriate conditions.Finally,the application to zero point problem of maximal monotone operators is given by the result.