Lipschitz局部强增殖算子的非线性方程的解的迭代构造

Iterative Construction of Solution to Nonlinear Equations of Lipschitzian and Local Strongly Accretive Operators

Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China

摘要: 本文研究p一致光滑Banach空间X中Ishikawa迭代法.设T:X→K是Lipschitz局部强增殖算子,方程T_x=f的解集sol(T)非空.我们证明了sol(T)是一个单点集且Ishikawa序列强收敛到方程T_x=f的唯一解.另行,当T是从X的非空凸子集K到X的Lipschitz局部伪压缩映像且T的不动点集F(T)非空时,我们证明了F(T)是一个单点集且Ishikawa序列强收敛到T的唯一不动点.我们的结果改进和推广了[4]与[5]的结果.
- 局部强增殖 /
- 局部严格伪压缩 /
- P一致光滑Banach空间
Abstract: In this paper,we investigate the Ishikawa iteration process in a p-uniformly smooth Banach space X.Let T:X→X be a Lipschitzian and local strongly accretive operator and the set sol(T) of solutions the equation T_x=f be nonempty.We show that soil(T) is a singleton atul the Ishikawa sequence converges strongly to the unique solution of the equation T_x=f.In addition,whenever T is a Lipschitzian and local Psendcontractive mapping from a nonempty convex subset K of X into X and the set F(T) of fixed points of T is nonempty,we prove that F(T) is a singleton and the Ishikawa sequetwe converges strongly to the unique fixed point of T.Our results are the improvements and extension of the results of Deng and Ding^[4] and Tan and Xu^[5].
- local strongly accretive /
- local strictly pseudocontractive /
- puniformly smooth Banach space

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