Convergence theorems for three finite families of multivalued nonexpansive mappings
Let \(K\) be a nonempty closed convex subset of a uniformly convex Banach space \(E\) and \(T_i, S_i, R_i:K\rightarrow CB(K)\), \(i=1,2,\dots,k\), be three finite families of multivalued nonexpansive mappings from \(K\) into \(CB(K)\), the collection of all nonempty closed bounded subsets of \(E\), such that \[ F:=(\bigcap_{i=1}^{k} \mathrm{Fix}\,(T_i))\cap (\bigcap_{i=1}^{k} \mathrm{Fix}\,(S_i))\cap (\bigcap_{i=1}^{k} \mathrm{Fix}\,(R_i)) \neq \emptyset, \] where \( \mathrm{Fix}\,(T_i)\) denotes the set of fixed points of \(T_i\). In order to approximate a common fixed point \(p\in F\), the authors consider a three step iterative scheme for which they prove weak and strong convergence theorems.
scientific article; zbMATH DE number 6363318
scientific article