Fixed point iteration for a countable family of multi-valued strictly pseudo-contractive-type mappings

This paper introduces a new averaged algorithm for finding a common fixed point of a countably infinite family of generalized k-strictly pseudocontractive multi-valued mappings. The new iterative sequence introduced is proved to be an approximating fixed point sequence for common fixed points of a countably infinite family of this class of mappings. Furthermore, under some mild assumptions, strong convergence theorems are also proved for this class of mappings. The method of proof used here is new and enables to overcome many strong restrictions appearing in contemporary literature. The stated theorems improve and generalize many recent works in iterative scheme for multi-valued mappings.