Two novel algorithms for solving variational inequality problems governed by fixed point problems and their applications
Shanshan Xu, Bing Tan, Songxiao Li · Fixed Point Theory · 2024
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 finiteand infinite-dimensional spaces are provided to illustrate the effectiveness and potential applicability of the suggested iterative methods compared to some known ones.