Viscosity approximative methods to Cesaro means for non-expensive mappings

In this paper, we defined viscosity iterative sequence {z(m)} and {x(n)} of the Cesaro means for non-expansive mappings T, and proved that {z(m)} and {x(n)} converge strongly to some p epsilon F(T), respectively, where p is a unique solution in F(T) to the following variational inequality: <(f-1)p,j(u-p)> <= 0 for all u is an element of 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: < http://www.sciencedirect.com/science/journal/00963003 > (accessed 28.02.06)]. (c) 2006 Elsevier Inc. All rights reserved.