Iteration by CesÀro Means for Quasi-Contractive Mappings

A. Razani, Z. Goodarzi

Let $C$ be a nonempty closed convex subset of a Banach space $E$ and $T$ be a quasi-contractive mapping on $C$. We prove, the sequence $\{x_n\}$, iteratively defined by, $$ \gather X_1\in C\\ y_n=s_nX_n+(1-s_n)T^nx_n\\ x_{n+1}=t_nx_n+(1-t_n)\frac1{n+1}\sum_{j=0}^nT^jy_n, \engether $$ is weakly convergent to a point of $F(T)$. Moreover, by a numerical example (using Matlab software), the main result and the rate of convergence are illustrated.