New strong convergence algorithms for general equilibrium and variational inequality problems and resolvent operators in Banach spaces

In this paper, we introduce two new algorithms for solving variational inequalities in Banach spaces. Our aim is finding a common element of the solution set of variational inequalities (for two inverse-strongly monotone operators) and an equilibrium problem and the set of fixed points of two relatively nonexpansive mappings and a family of resolvent operators. Then the strong convergence of the sequences generated by these algorithms to this element will be proved under suitable conditions. Finally, we provide a numerical example to illustrate our main results.