自反Banach空间中右Bregman强非扩张映射的强收敛定理

Strong convergence theorem for right Bregman strongly nonexpensive mappings in reflexive Banach spaces

摘要:

在实自反的Banach空间中,针对有限族右Bregman强非扩张映射公共不动点构造了一类新型的Mann-Halpern型迭代算法,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 introduce Mann-Halpern algorithm for finding a common fixed point problem of finite family of right Bregman strongly nonexpansive mappings in reflexive mappings in reflexive real Banach spaces.Moreover,we prove a strong convergence theorem under suitable control conditions.Finally,the application to a common zero of a finite family of maximal monote mappings is given by the result.