Xu和Norr已经证明了建立在一致凸Banach空间的一个非空有界闭凸子集上的渐进非扩张映射的三步迭代的收敛定理问题.引入(L-α)一致李普希兹的概念,然后在一些已有结果的基础上,证明一致凸Banach空间的紧子集上的(L-α)一致李普希兹渐进非扩张映射的三步迭代序列的收敛问题.这个结论是对Xu和Noor的相应结果的推广.
Xu and Noor had proved the theorem on convergence of three-step iterations for asymptotically nonexpansive mapping on nonempty closed, bounded, and convex subset of uniformly convex Banach space. Based on some results given by K Tan and H K Xu[1] proved, the convergence of three-step iterations of (L-α) uniformly Lipschitz asymptotically nonexpansive mapping on a compact subset of a uniform convex Banach space had proved. The results presented extended the corresponding of Xu and Noor[5].
[1] Tan K, XU H K. Fixed point iteration processes for asymptotically nonexpansive mapping [J]. Proceedings of the American Mathematical Society 1994, 122.
[2] GOSH M K, DEBNATH L. Convergence of Ishikawa iterations of quasi-nonexpansive mapping [J]. Journal of Mathematical Analysis and Applications 1997, 207.
[3] LIU QIHOU. Iteration sequences for asymptotically quasi-nonexpansive mapping with erro member of uniform convex Banach Space [J]. Journal of Mathematical Analysis and Applications 2002, 266.
[4] Xu H K. Existence and convergence for fixed points mapping of asymptotically nonexpansive type [J]. Nonlinear Analysis 1991, 16.
[5] XU BENLONG. Fixed-point iterations for asymptotically nonexpansive mapping in Banach Space [J]. Journal of Mathematical Analysis and Applications 2002, 267.
