Banach空间中φ-半压缩映象的Ishikawa迭代过程

Ishikawa Iterative Process for φ-Hemicontractive Mapping in Banach Space

设X是任意实Banach空间 ,K是X的非空凸子集且K+K K ,T :K→K是值域有界且一致连续的φ-半压缩映象 ,则Ishikawa迭代过程强收敛到T的唯一不动点。由此可知 ,若T是 φ -强拟增生映象 ,则Ishikawa迭代序列强收敛到方程Tx =0的唯一解。

Let x be a real Banach space, K a Nonempty convex subset of x and K+KK . Let T:K→K be a uniformly continuous φ_hemicontractive mapping with bounded codomain range,then the Ishikawa iterative sequence converges strongly to the unique fixed point of T . Thus it can be seen if T is φ _strongly quasi_accretive mapping,then Islikawa iterative sequence converges strongly to the unique solution of equation Tx =0