LAUSR

. We study the problem of finding a common solution to the variational inequality problem with a pseudomonotone and Lipschitz continuous operator and the fixed point problem with a demicontractive mapping in real Hilbert spaces. Inspired by the inertial method and the subgradient extragradient method, two improved viscosity-type efficient iterative methods with a new adaptive non-monotonic step size criterion are proposed. We prove that the strong convergence theorems of these new methods hold under some standard and mild conditions. Numerical examples in finite-and infinite-dimensional spaces are provided to illustrate the effectiveness and potential applicability of the suggested iterative methods compared to some known ones.