关于一致光滑Banach空间中的Ishikawa迭代

Ishikawa Iterative Process in Uniformly Smooth Banach Spaces

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 xn 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·

Let E be a uniformly smooth Banach s pace, K be a nonempty closed convex subset of E, and suppose: T:K→K is a continuous Φ-strongly pseudocontractive operator with a bounded ran ge. Using a new analytical method, under general cases, the Ishikawa iterative p rocess x n converges strongl y to the unique fixed point x~* of the operator T were proved. The pape r generalizes and extends a lot of recent corresponding results.