Implicit iteration process of nonexpansive non-self-mappings (Q2368430)

The authors study the convergence of the sequences \(\{x_n\}\), \(\{y_n\}\), \(\{z_n\}\) satisfying \(x_n =(1-\alpha_n ) u + \alpha_n TP[(1-\beta_n)x_n +\beta_n T x_n]\), \(y_n =(1-\alpha_n ) u + \alpha_n PT[(1-\beta_n)y_n +\beta_n PT y_n]\) and \(z_n =P[(1-\alpha_n ) u + \alpha_nTP[(1-\beta_n)z_n +\beta_n T z_n]]\), where \(\{ \alpha_n \} \subset (0,1)\), \(0 \leq \beta_n \leq \beta <1\) and \(\alpha_n \to 1\) as \(n \to \infty\). Their results extend and improve a host of results in the recent literature.