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

Abstract

Abstract:

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.

Key words: Fixed point, Variational inequality, Strong convergence, Nonexpansive mapping, Banach space

CLC Number:

O177.91

Cai Gang. Strong Convergence Theorems by A Viscosity Iterative Method for Fixed Point Problems of Nonexpansive Mappings in Banach Spaces[J].Acta mathematica scientia,Series A, 2015, 35(3): 487-502.

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

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