Viscosity approximative methods to Cesàro means for non-expansive mappings

摘要

In this paper, we defined viscosity iterative sequence {zm} and {xn} of the Cesàro means for non-expansive mappings T, and proved that {zm} and {xn} converge strongly to some p ∈ F(T), respectively, where p is a unique solution in F(T) to the following variational inequality:〈(f-I)p,j(u-p)〉⩽0for allu∈F(T).Our results developed and complemented the corresponding ones by Shin-ya Matsushita and Daishi Kuroiwa [Strong convergence of averaging iterations of nonexpansive nonself-mappings, J. Math. Anal. Appl. 294 (2004) 206–214] and H.K. Xu [Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl. 298 (2004) 279–291] and Yongfu Su and Suhong Li [Strong convergence theorems on two iterative method for non-expansive mappings, Appl. Math. Comput. Available from: (accessed 28.02.06)].