Convergence theorems of common fixed points for a family of Lipschitz quasi-pseudocontractions

In an infinite-dimensional Hilbert space, the normal Mann’s iteration has only weak convergence, in general, even for nonexpansive mappings. The purpose of this paper is to modify the normal Mann’s iteration to have strong convergence for a family of Lipschitz quasi-pseudocontractions in the framework of Hilbert spaces. Our results improve and extend the corresponding ones announced by many others.