Improved subgradient extragradient methods for solving pseudomonotone variational inequalities in Hilbert spaces

The purpose of this work to investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces. For solving problem, we propose two new methods which combine advantages the subgradient extragradient method projection contraction method. Similar some recent developments, proposed do not require knowledge constant associated with inequality mapping. Under suitable mild conditions, establish weak strong convergence algorithms. Moreover, linear is obtained under pseudomonotonicity continuity assumptions. Numerical examples fractional programming optimal control problems demonstrate potential our algorithms as well compare their performances several related results.