On weak and strong convergence results for generalized equilibrium variational inclusion problems in Hilbert spaces
Shahram Rezapour, Seyyed Hasan Zakeri · Advances in Difference Equations · 2020
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\in \varOmega $ p ∈ Ω which is the unique solution of a variational inequality, where Ω is an intersection of set as given by ${\varOmega }=F(S)\cap (A+B)^{-1}(0) \cap N^{-1}(0)\cap \operatorname{GEP}(F,M) eq \emptyset $ 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.