混合Bregman投影算法在Banach空间中分裂不动点问题的强收敛性

Strong Convergence of Hybrid Projection Algorithm for Split Fixed Point Problems in Banach Spaces

在p-一致凸且一致光滑的Banach空间中,利用Bregman投影,构造一新的混合投影迭代算法,逼近Bregman拟严格伪压缩映射不动点集和分裂可行性问题的公共解.目的是将2017年Chen J Z,Hu H Y和Ceng L C的研究结果中的迭代系数α_(n)须满足0<c≤a_(n)≤d<1证明对α_(n)≡1或α_(n)≡0时亦成立.所得的结果是对2017年Chen J Z,Hu H Y和Ceng L C相应结果的拓展和补充.

In p-uniformly convex and uniformly smooth Banach space,a new iterative algorithm is constructed to approximate the fixed point set of Bregman quasi-strict pseudocontractive mapping and the common solution of split feasibility problem by the Bregman projection.It is proved that the iterative coefficient α_(n) which is considered to satisfy 0<c<α_(n)≤d<1 in the earlier research results(Chen J Z,Hu H Y,and Ceng L C in 2017)also does work for α_(n)≡1 or α_(n)≡0.Thus,this study not only serves as complement to the former results,but importantly,update their conclusion.