Strong convergence theorems for strict pseudo-contractions in \(q\)-uniformly smooth Banach spaces
Let \(C\) be a closed convex subset of a real \(q\)-uniformly smooth Banach space and \(T_i:C\to C\), \(i=1,2,\dots,N\), be a finite family of mappings which are strictly pseudo-contractive. Assume that \(F:= \bigcap^N_{i=1}F(T_i)\neq\emptyset\). Let \(u,x_0\in C\) be arbitrary fixed vectors in \(C\). It is proved that the sequence \(\{x_n\}_{n\geq 0}\) generated by \[ \begin{cases} y_n=(1-\alpha_n)x_n+\alpha_n \sum^N_{i=1} \eta_i^{(n)}T_ix_n,\\ x_{n+1}=\beta_nu+\gamma_nx_n+\delta_ny_n, \end{cases} \] where \(\{\alpha_n\}\), \(\{\beta_n\}\), \(\{\gamma_n\}\) and \(\{\sigma_n\}\) are sequences in \((0,1)\) satisfying appropriate conditions, converges strongly to an element of \(F\).
scientific article; zbMATH DE number 5539203
scientific article