Banach空间中广义Lipschitz Φ-强伪压缩映射的Ishikawa迭代逼近

Ishikawa Iterative Approximation for Generalized Lipschitzian Φ-Strongly Pseudocontracive Mappings in Banach Spaces

设1<q≤2,T是从实q-一致光滑Banach空间E的非空闭凸子集到自身的广义Lipschitz Φ-强伪压缩映射,且有不动点.证明了Ishikawa迭代强收敛到T的唯一不动点.

Let 1 〈 q≤2, suppose T is a generalized Lipschitzian φ-strongly pseudocontractive self-mapping on a nonempty closed convex subset of a real q-uniformly smooth Banach space E, and has a fixed point. It is shown that the Ishikawa iterarive method converges strongly to the unique fixed point of T.