一致L-Lipschitz渐近Φ-半压缩映像不动点迭代逼近的充要条件

The sufficient and necessary condition of iterative approximation to the fixed points of uniformly L-Lipschitzian asymptotically Φ-hemi-contractive mappings

在任意实Banach空间中,讨论一致L-Lipschitz渐近Φ-半压缩映像不动点的Ishikawa迭代逼近问题.利用一致L-Lipschitz有关不等式及新的分析方法,得到了具误差的修正的Ishika-wa迭代序列逼近渐近Φ-半压缩映像不动点的充要条件,改进推广了一些文献的相关结论.

The problem of iterative approximation to the fixed points of uniformly L-Lipschitzian asymptotically Φ-hemi-contractive mappings are discussed in arbitrary Banach space.By using corresponding inequality of uniformly L-Lipschitzian and new analysis methods,a sufficient and necessary condition of modified Ishikawa iterative sequence with error approximation asymptotically Φ-hemi-contractive mappings is obtained,and some related conclusions are improved and generalized.