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An up-to-date method is used for approximating common fixed points of countable families of nonlinear mappings. A modified Picard-Mann hybrid iterative algorithm is introduced with the help of our method for the class of nonexpansive mappings. Strong convergence and weak convergence theorems are established in the framework of uniformly convex Banach spaces. Our results extend the corresponding ones announced by Khan (Fixed Point Theory Appl. 2013:69, 2013, doi:10.1186/1687-1812-2013-69) to the case of countable families of nonexpansive mappings.

A modified Picard-Mann hybrid iterative algorithm for common fixed points of countable families of nonexpansive mappings