Stability and convergence of modified Ishikawa iterative sequences with errors in Banach spaces (Q2495682)

The authors investigate the convergence and stability properties (almost T-stability and weakly T-stability) of the following sequences: the modified Ishikawa iterative sequence with errors \(\{x_n\}\subset E\) defined by \[ \begin{cases} x_{n+1}=(1-\alpha_n)x_n+\alpha_nT^ny_n+u_n,\cr y_n=(1-\beta_n)x_n+\beta_nT^nx_n+v_n,\;n\geq 0,\end{cases} \] the modified Ishikawa iterative sequence with mean errors \(\{x_n\}\subset E\) defined by \[ \begin{cases} x_{n+1}=(1-\alpha_n-\gamma_n)x_n+\alpha_nT^ny_n+\gamma_nu_n,\cr y_n=(1-\beta_n-\delta_n)x_n+\beta_nT^nx_n+\delta_nv_n,\;n\geq 0,\end{cases} \] and the modified Ishikawa iterative sequence \(\{x_n\}\subset E\) defined by \[ \begin{cases} x_{n+1}=(1-\alpha_n)x_n+\alpha_nT^ny_n,\cr y_n=(1-\beta_n)x_n+\beta_nT^nx_n,\;n\geq 0.\end{cases} \] Here, \(E\) is a real Banach space and \(T:D(T)\subset E\to E\) is a (strictly) asymptotically pseudo-contractive mapping and asymptotically nonexpansive in the intermediate sense or it is a strictly asymptotically pseudo-contractive mapping and uniformly Lipschitzian.