Strong convergence on iterative methods of Cesàro means for nonexpansive mapping in Banach space (Q1722336)

Summary: Two new iterations with Cesàro's means for nonexpansive mappings are proposed and the strong convergence is obtained as \(n \rightarrow \infty\). Our main results extend and improve the corresponding results of \textit{H.-K. Xu} [J. Math. Anal. Appl. 298, No. 1, 279--291 (2004; Zbl 1061.47060)], \textit{Y.-S. Song} and the second author [Appl. Math. Comput. 186, No. 2, 1120--1128 (2007; Zbl 1121.65063)], and \textit{Y.-H. Yao} et al. [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 6, 2332--2336 (2009; Zbl 1223.47107)].