关于非扩张映射的不动点问题的粘性迭代算法的强收敛定理

Strong Convergence Theorems by A Viscosity Iterative Method for Fixed Point Problems of Nonexpansive Mappings in Banach Spaces

该文首先研究吸引非扩张映射的性质,然后在一致光滑Banach空间里,用这些性质研究两个非扩张映射的不动点问题的粘性迭代算法.作为应用,在Banach空间或Hilbert空间里,得到了关于变分不等式问题,不动点问题和均衡问题的强收敛定理.所得结果提高和推广了许多最近的相关结果.

In this paper, we first study some properties of attracting nonexpansive mappings. Furthermore, we use these properties to investigate some viscosity iterative methods for fixed point problems of two nonexpansive mappings in uniformly smooth Banach space. As an application, we obtain some strong convergence theorems for variational inequality problems, fixed point problems and equilibrium problems in Banach spaces or Hilbert spaces. The results obtained in this paper improve and extend many recent ones announced by many others in this literature.