New strong convergence algorithms for general equilibrium and variational inequality problems and resolvent operators in Banach spaces - Ghadampour, Mostafa; Soori, Ebrahim; Agarwal, Ravi P.; O’Regan, Donal (Nonlinear Analysis: Modelling and Control, 2026)
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.
Keywords: relatively nonexpansive mapping; fixed point problem; equilibrium problem; inverse-strongly monotone operator; maximal monotone operator