关于一致光滑Banach空间中的Ishikawa迭代

基金项目: 国家自然科学基金(青年基金)资助项目(19801017);教育部骨干教师资助项目

Ishikawa Iterative Process in Uniformly Smooth Banach Spaces

摘要: 设E为一致光滑Banach空间,K为E的非空闭凸子集,T:K→K为具有有界值域的连续Φ-强伪压缩算子。使用新的分析技巧证明了在非常普遍的条件下,Ishikawa迭代序列{x_n}强收敛于T的唯一不动点x^*。改进和扩展了近期许多相关的结果。
- Ishikawa迭代 /
- Φ-强伪压缩算子 /
- 一致光滑Banach空间
Abstract: Let E be a uniformly smooth Banach space,K be a nonempty closed convex subset of E, and suppose:T:K→K is a continuous 5-strongly pseudocontractive operator with a bounded range. Using a new analytical method,under general cases,the Ishikawa iterative process {x_n} converges strongly to the unique fixed point x^* of the operator T were proved.The paper generalizes and extends a lot of recent corresponding results.
- Ishikawa iterative process /
- Φ-stongly pseudocontractive operators /
- uniformly smooth Banach spaces

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