Strong and \(\Delta\)-convergence theorems for common fixed points of a finite family of multivalued demicontractive mappings in CAT\((0)\) spaces
Summary: Let \(K\) be a nonempty closed and convex subset of a complete CAT(0) space. Let \(T_i : K \rightarrow \text{C} \text{B} \left(K\right)\), \(i = 1,2, \dots, m\), be a family of multivalued demicontractive mappings such that \(F : = \bigcap_{i = 1}^m F(T_i) \neq \varnothing\). A~Krasnoselskii-type iterative sequence is shown to \(\Delta\)-converge to a common fixed point of the family \(\left\{T_i, i = 1,2, \dots, m\right\}\). Strong convergence theorems are also proved under some additional conditions. Our theorems complement and extend several recent important results on approximation of fixed points of certain nonlinear mappings in CAT\((0)\) spaces. Furthermore, our method of the proof is of special interest.
scientific article; zbMATH DE number 7023110
scientific article