无穷个m增生映射和逆强增生映射的隐式单调投影算法与p-Laplacian系统

Implicit monotone projection scheme for infinite m-accretive mappings and inversely strongly accretive mappings and p-Laplacian systems

首先在Hilbert空间中,设计了带误差项的隐式单调投影迭代算法,证明了迭代序列强收敛到无穷个非线性m增生映射与逆强增生映射和的公共零点的结论,将以往的相关研究成果从有限个映射的情形推广到无穷个;其次采用分裂法将一类p-Laplacian型抛物系统转化成算子方程的形式,证明了p-Laplacian型抛物系统非平凡解的存在性并建立了非平凡解与无穷个m增生映射与逆强增生映射和的公共零点的关系;最后构造了p-Laplacian型抛物系统非平凡解的迭代逼近序列,推广和补充了以往的相关研究成果.

In the paper, an implicit monotone projection iterative scheme with errors is designed in Hilbert spaces. The iterative sequence is proved to be strongly convergent to the common zero of the sum of infinite family of m-accretive mappings and inversely strongly accretive mappings, which extends the previous corresponding studies from the finite cases to infinite ones. Secondly, by using splitting methods, one kind of p-Laplacian-like parabolic systems is converted to operator equations. The existence of the non-trivial solution of the p-Laplacian-like parabolic systems is obtained and the relationship between the non-trivial solution and the common zero of the sum of infinite m-accretive mappings and inversely strongly accretive mappings is being set-up. Finally, the iterative approximate sequence of the non-trivial solution of the p-Laplacian-like parabolic systems is constructed. The work done in this paper extends and complements some previous corresponding work.