Strong convergence of iteration algorithms for a countable family of nonexpansive mappings

Abstract: For a countable family of nonexpansive mappings, a strong convergence of Halpern type iteration is shown in order to find a common fixed point of in a reflexive Banach space when satisfies the conditions (C1) and (C2) , and several examples satisfying the condition (B) is given also. We also research the strong convergence of the proximal point algorithm. Finally, we apply our results to solve the equilibrium problems and variational inequalities for continuous monotone mappings. [Copyright &y& Elsevier]