Iterative Schemes for Fixed Points of Relatively Nonexpansive Mappings and Their Applications

摘要

We present two iterative schemes with errors which are proved to be strongly convergentto a common element of the set of fixed points of a countable family of relatively nonexpansive mappingsand the set of fixed points of nonexpansive mappings in the sense of Lyapunov functional in a real uniformlysmooth and uniformly convex Banach space. Using the result we consider strong convergence theorems forvariational inequalities and equilibrium problems in a real Hilbert space and strong convergence theoremsfor maximal monotone operators in a real uniformly smooth and uniformly convex Banach space.