Algorithms for finding a common element of the set of common fixed points for nonexpansive semigroups, variational inclusions and generalized equilibrium problems

Abstract

In this work, we introduced an iterative algorithm for finding a common element of the set of common fixed points of a one-parameter nonexpansive semigroup, the set of solutions to a variational inclusion and the set of solutions to a generalized equilibrium problem in a real Hilbert space. Furthermore, we proved the convergence theorem of the proposed iterative algorithm under some mild conditions on algorithm parameters. Finally, we gave some numerical examples which support our main theorem at last part. The results presented in this paper generalize the well-known theorems.