没有Lipschitz假设的ψ-半压缩映象的不动点与ψ-强拟增生算子方程解的逼近

设X为实一致光滑Banach空间,T:D(T)∈X→X为ψ-半压缩映象且在它的不动点q处是局部有界的.本文证明了Mann迭代与Ishikawa迭代过程强收敛于T的唯一不动点g.几个相关的结果处理ψ-强拟增生算子方程的解的迭代构造.本文所得到的结果扩展并推广了Xu和Roach,Zhou和Jia等人的相应结果.

Approximation of Fixed Point and Solution for ψ-Hemicontraction and ψ-Strongly Quasi-Accretive Operator without Lipschitz Assumption

Let X be a real uniformly smooth Banach space and let T: D(T)∈ X → X be ψ-hemicontractive and locally bounded at its fixed point q ∈ F(T). Under some suitable assumptions on the iteration parameters {αn} and {βn }, we have proved that the Mann and Ishikawa iteration processes for T converge strongly to the unique fixed point q of T. Several related results deal with iterative solutions of nonlinear equations involving o-strongly quasi-accretive operators. Our results extend and generalize those corresponding ones by Xu and Roach, Zhou and Jia and others.