Strong convergence theorems for a pair of strictly pseudononspreading mappings (Q2337036)

Summary: Let \(H\) be a real Hilbert space. Let \(T_1, T_2 : H \to H\) be \(k_1\)-, \(k_2\)-strictly pseudononspreading mappings; let \(\{\alpha_n\}\) and \(\{\beta_n\}\) be two real sequences in \((0,1)\). For given \(x_0 \in H\), the sequence \(\{x_n\}\) is generated iteratively by \(x_{n + 1} = \beta_n x_n + (1-\beta_n) T_{w_1}(\alpha_n \gamma f (x_n) + (I - \mu \alpha_n B) T_{w_2} x_n)\), \(n \in N\), where \(T_{w_i} =(1 - w_i) I + w_i T_i\) with \(i = 1,2\) and \(B : H \to H\) is strongly monotone and Lipschitzian. Under some mild conditions on parameters \(\{\alpha_n\}\) and \(\{\beta_n\}\), we prove that the sequence \(\{x_n\}\) converges strongly to the set \(F_{i x}(T_1) \cap F_{i x} (T_2)\) of fixed points of a pair of strictly pseudononspreading mappings \(T_1\) and \(T_2\).