Iterative convergence to Cesaro means for continuous pseudocontractive mappings

Let f be a fixed strongly pseudocontractive mapping and T be a continuous pseudocontractive mapping with F(T) not equal empty set. The sequence {z(m)} is iteratively defined as follows: z(m) = t(m)f(z(m)) + (1 - t(m)) 1/m + 1 (j=0)Sigma(m) T(j)z(m), m >= 0, where {t(m)} subset of (0, 1) satisfies the condition lim(m ->infinity) t(m) = 0. We prove that {z(m)} converges strongly to the unique solution p to some variational inequality in F(T). Our results develop and complement the corresponding ones by Matsushita-Daishi Kuroiwa [J. Math. Anal. Appl. 294 (2004) 206-214] and Shioji-Takahashi [Arch. Math., 72 (1999) 354-359] and Moore-Nnoli [J. Math. Anal. Appl. 260 (2001) 269-278] and Su-Li [Appl. Math. Comput. 181 (2006) 332-341] and Song-Chen [Appl. Math. Comput. 186 (2007) 1120-1128] and Wangkeeree [Appl. Math. Comput. 201 (2008) 239-249]. (C) 2009 Elsevier Ltd. All rights reserved.