  The objective of this research is to explore a convex feasibility problem,
which consists of a monotone variational inequality problem and a fixed point
problem. We introduce four inertial extragradient algorithms that are motivated
by the inertial method, the subgradient extragradient method, the Tseng's
extragradient method and the Mann-type method endowed with a simple step size.
Strong convergence theorems of the algorithms are established under some
standard and suitable conditions enforced by the cost operators. Finally, we
implement some computational tests to show the efficiency and advantages of the
proposed algorithms and compare them with some existing ones.
