SHRINKING PROJECTION METHODS FOR A FAMILY OF RELATIVELY NONEXPANSIVE MAPPINGS, EQUILIBRIUM PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS IN BANACH SPACES - Plubtieng, S.; Thammathiwat, T. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2011)
In this paper, we prove a strong convergence theorem by the shrinking projection method for finding a common element of the set of fixed points of a countable family of relatively nonexpansive mappings and the set of solutions of equilibrium problems and the set of solution of variational inequality problems in Banach spaces. Then, we apply our main theorem to the problem of finding a zero of a maximal monotone operator, the complementarity problems, and the convex feasibility problems.