Cyclic algorithm for common fixed points of finite family of strictly pseudocontractive mappings of Browder-Petryshyn type
The authors prove weak and strong convergence theorems for finitely many strict pseudocontractions \(T_1,\dots,T_N\) of a closed convex subset \(K\) of a 2-uniformly smooth and uniformly convex Banach space by the iterative scheme: \(x_1\in K\) and \(x_{n+1}=\alpha_n x_n+(1-\alpha_n)T_{n\text{mod}\,N}\), where \(\{\alpha_n\}\) is an appropriate sequence in \([0,1]\). A necessary and sufficient condition for the strong convergence of the sequence \(\{x_n\}\) to a common fixed point of the family of mappings is also proved.
scientific article; zbMATH DE number 5543761