1Department of Mathematics, Statistics and Computer,
Faculty of Science, Ubon Ratchathani University, Ubon Ratchathani
Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand
We prove a strong convergence result for a sequence generated by Halpern's 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.