Hilbert空间中非扩张余弦族的显式、隐式和黏性迭代

Explicit,Implicit and Viscosity Iterations for Nonexpansive Cosine Families in Hilbert Spaces

研究了Hilbert空间中一些逼近单参数非扩张余弦族公共不动点的迭代格式.借助余弦族理论,在较弱的条件下分别对显式、隐式和黏性的迭代过程建立了一系列的收敛定理.结果表明上述三种迭代过程适用于非扩张余弦族;并且隐式和黏性迭代格式在收敛性上优越于显式迭代格式.

In this paper some iterative schemes to approximate a common fixed point of oneparameter nonexpansive cosine family are investigated in Hilbert spaces. By using the theory of cosine families, a series of new convergence theorems are established under some mild conditions for the explicit, implicit and viscosity iteration processes, respectively. Our results show that the above three iterative methods are applicable to the nonexpansive cosine families; and the implicit and viscosity iterations are superior the explicit iteration in convergence.