Strong convergence of a new composite iterative method for equilibrium problems and fixed point problems in Hilbert spaces

摘要

In this paper, first we introduce a new mapping for finding a common fixedpoint of an infinite family of nonexpansive mappings then we consider iterativemethod for finding a common element of the set of fixed points of an infinitefamily of nonexpansive mappings, the set of solutions of an equilibrium problemand the set of solutions of the variational inequality for$\alpha$-inverse-strongly monotone mapping in a Hilbert space. We show thatunder suitable conditions, the sequence converges strongly to a common elementof the above three sets. Our results presented in this paper improve and extendother results.