An improved relaxed inertial projection algorithm for solving the minimum-norm solution of variational inequality and fixed point problems

In this paper, a modified projection algorithm is proposed in order to solve a common element of the solution set of monotone variational inequality and the fixed point set of a class of quasi-pseudo-contractive mapping. This algorithm requires the monotonicity and Lipschitz continuity of the mapping, but don’t need to know Lipschitz constant. On one hand, this algorithm does not compute the projection onto the feasible set at each iteration, on the other hand, the strong convergence of the sequence generated by the algorithm can be obtained without viscosity technology, and the convergence rate of the algorithm better than some algorithms, and the effect of the algorithm is illustrated by two numerical experiments.