具有Fréchet可微范数的实一致凸Banach空间中可数严格伪压缩映射族的弱收敛定理

Weak Convergence Theorems for a Countable Family of Strict Pseudocontraction Mappings in a Uniformly Convex Banach Space with the Fréchet Differentiable Norm

为了研究在具有Fréchet可微范数的实一致凸Banach空间中的可数的严格伪压缩映射族Mann型迭代方案的收敛性,利用Marino-Xu,Zhou,Osilike-Udomene,Zhang-Guo的结论以及其它相关的结论,在已有结论的基础上,将Chidume-Shahzad的某些结论推广到具有Fréchet可微范数的实一致凸Banach空间的无限严格伪压缩映射族的情形下,并给出了在具有Fréchet可微范数的实一致凸Banach空间中的可数严格伪压缩映射族的Mann型迭代方案弱收敛性的证明。

In this paper,in order to investigate the convergences of Mann-type iterative scheme for a countable family of strict pseudocontraction mappings in a uniformly convex Banach space with the Fréchet differentiable norm,we used the results obtained by Marino-Xu,Zhou,Osilike-Udomene,Zhang-Guo and the corresponding results to extend some conclusions obtained by Chidume-Shahzad to the real uniformly convex Banach space with the Fréchet differentiable norm under the countable strictly pseudocontraction mappings.And the proof of the weak convergences of Mann-type iterative scheme for a countable family of strict pseudocontraction mappings in this Banach space with the Fréchet differentiable norm was given.