关于一致φ-伪压缩映射的4种迭代收敛程序的等价性(英文)

On the equivalence of the convergence about four iterations for uniformly φ-pseudocontractive mapping

一致φ-伪压缩映射是伪压缩类映射中最广泛的一种映射.讨论了一致φ-伪压缩映射的Mann迭代、Ishikawa迭代、具误差的Mann迭代、具误差的Ishikawa迭代收敛程序的等价性.所研究的定理是在较为广义的映射下的4种迭代收敛程序的等价性,因而该结论推广和改进了相关的结果.

Abstract： In this paper, the equivalence of the convergence about Mann iterations, Ishikawa iterations, Mann iterations with errors and Ishikawa iterations with errors is proved for the unifomly Ф-pseudocontractive operator. The uniformly Ф-pseudocon- tractive operator is the most widely of all pseudocontractive operators. Our results generalize and improve the corresponding re- sults by extending to the more generalized four iterations and uniformly Ф-pseudocontractive operator.