中文摘要：

在任意实赋范线性空间中，引入了一个新型的带误差的修正的三步迭代序列{xn），在不限制“{xn）有界”的条件下，证明了该迭代序列强收敛于一致Lipschitz渐近伪压缩映像T的不动点，且给出了该迭代序列强收敛的必要条件．其结果改进和推广了其他一些相应的近代结果，且证明方法也与以往的有所不同．

英文摘要：

In this paper, we give a new modified three-step iterative sequence {x~ } with errors in an arbitrary real norm linear space. Without the boundedness condition of the sequence {xn}, we prove that the sequence converges strongly to a fixed point of a uniformly Lipschitzian asymptotically pseudo-contractive mapping T. We also point out the necessary condition of the strong convergence for the iterative sequence. The results extend and improve some corresponding related results and the proof method is different from that by using mathematical induction.