A class of strongly convergent subgradient extragradient methods for solving quasimonotone variational inequalities

Abstract The primary goal of this research is to investigate the approximate numerical solution variational inequalities using quasimonotone operators in infinite-dimensional real Hilbert spaces. In study, sequence obtained by proposed iterative technique for solving converges strongly toward a due viscosity-type scheme. Furthermore, new that uses an inertial mechanism obtain strong convergence iteratively without requirement hybrid version. fundamental benefit suggested strategy it substitutes monotone and non-monotone step size rule based on mapping (operator) information its Lipschitz constant or another line search method. This article also provides example demonstrate how each method works.