Convergence theorems for infinite family of multivalued quasi-nonexpansive mappings in uniformly convex Banach spaces (Q417150)

Summary: We introduce an iterative method for finding a common fixed point of a countable family of multivalued quasi-nonexpansive mapping \(\{T_i\}\) in a uniformly convex Banach space. We prove that under certain control conditions, the iterative sequence generated by our method is an approximating fixed point sequence of each \(T_i\). Some strong convergence theorems of the proposed method are also obtained for the following cases: all \(T_i\) are continuous and one of \(T_i\) is hemicompact, and the domain \(K\) is compact.