Iterative methods for finding nearest common fixed points of a countable family of quasi-Lipschitzian mappings

We prove a strong convergence result for a sequence generated by‎ ‎Halpernʹs type iteration for approximating a common fixed point of a‎ ‎countable family of quasi-Lipschitzian mappings in a real Hilbert‎ ‎space‎. ‎Consequently‎, ‎we apply our results to the problem of finding‎ ‎a common fixed point of asymptotically nonexpansive mappings‎, ‎an‎ ‎equilibrium problem‎, ‎and a variational inequality problem for‎ ‎continuous monotone mappings‎.