摘要
非线性算子的不动点理论和变分不等式理论在数学中已有较突出的地位,其最重要也很有趣的内容是利用非线性算子理论构造迭代算法,最后证明迭代算法的收敛性。鉴于此,本文从以下几个方面讨论:
1.简述非线性算子理论的历史背景和研究现状。
2.介绍和研究了l_p空间中严格伪压缩映射Mann迭代序列的弱收敛性。
3.在Hilbert空间中引入和研究了连续伪压缩映射的一新的广义迭代算法,并证明了这类迭代算法的收敛性。
Fixed point of nonlinear operator theory and variational inequality theory have been prominent in mathematics. Among many aspects of it, the most important and interesting is to develop effective numerical methods to generate approximate solutions. This paper will discuss it in the following way:
Firstly, the background and current state of nonlinear operator theory will be discussed.
Secondly, it will introduces and studies weakly convergence to Mann iteration process for strict pseudo-contraction in l_p space.
Thirdly, it will introduces and studies a new general iterative method for continuous pseudocontractive mappings in Hilbert spaces .
引文
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