On weak and strong convergence results for generalized equilibrium variational inclusion problems in Hilbert spaces

Abstract We introduce a new iterative method for finding a common element of the set of fixed points of pseudo-contractive mapping, the set of solutions to a variational inclusion and the set of solutions to a generalized equilibrium problem in a real Hilbert space. We provide some results about strongly and weakly convergent of the iterative scheme sequence to a point p p ∈ Ω which is the unique solution of a variational inequality, where Ω is an intersection of set as given by =F (S) (A+B) ^-1 (0) N^-1 (0) GEP (F, M) Ω = F (S) ∩ (A + B) − 1 (0) ∩ N − 1 (0) ∩ GEP (F, M) ≠ ∅. This gives us a common solution. Also, We show that our results extend some published recent results in this field. Finally, we provide an example to illustrate our main result.