关于Lipschitz严格伪压缩映象的带误差的Ishikawa型迭代程序-重庆师范大学学报（自然科学版）

文章信息/Info

Title:: On the Ishikawa Iteration Process with Errors for Lipschitz Strictly Pseudocontractive Mappings

作者:: 龙宪军1; 彭再云2; 敖　军3; 1.重庆工商大学　数学与统计学院，重庆 400067；2.重庆交通大学　理学院，重庆 400074；
3.重庆师范大学　数学与计算机科学学院，重庆 400047

Author(s):: LONG Xian-jun1; PENG Zai-yun2; AO Jun3; 1.College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067；
2.College of Science, Chongqing Jiaotong University, Chongqing 400074；
3.College of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China

摘要:: 设K是任意实Banach空间X中的闭凸子集，T：K→K是Lipschitz严格伪压缩映象，在没有假设＜∞之下，本文证明了由xn+1=(1－αn) xn+αnTyn+un与yn＝(1－βn) xn+βnTxn+vn, n∈N，生成的带误差的Ishikawa迭代序列强收敛到T的唯一不动点，并给出了更为一般的收敛率估计：若un=vn=0, n∈N，则有‖xn+1－x*‖≤(1－γn) ‖xn－x*‖≤…≤ (1－γj) ‖x0－x*‖，其中｛γn｝是(0,1)中的序列，满足γn≥ min(ε，η－ε) αn。所得结果改进和推广了最新的一些结果。

Abstract:: Let K be a closed convex subset of an arbitrary real Banach space X，and T：K→K be a Lipschitz strictly pseudocontractive mapping such that T x*= x* for some x*∈X. Under the lack of the assumption that ＜∞，it is shown that the Ishikawa iterative sequence with errors engendered by xn+1=(1－αn) xn+αnTyn+un and yn＝(1－βn) xn+βnTxn+vn, for all n∈N，converges strongly to the unique fixed point of T. Moreover, this result provides a general converges rate estimate for such a sequence: if un=vn=0, for all n∈N，then we have ‖xn+1－x*‖≤(1－γn) ‖xn－x*‖≤…≤ (1－γj) ‖x0－x*‖，where ｛γj｝is a sequence in (0,1) such that for all n∈N, γn≥ min(ε，η－ε) αn. These results improve and generalize the recent corresponding results.