An Iterative Algorithm for Solving Fixed Point Problems and Quasimonotone Variational Inequalities

In this paper, we survey a common problem of the fixed point problem and the quasimonotone variational inequality problem in Hilbert spaces. We suggest an iterative algorithm for finding a common element of the solution of a quasimonotone variational inequality and the fixed point of a pseudocontractive operator. Convergence theorems are shown under some mild conditions. Several corollaries are also obtained.

Automated summary

In this paper, we investigate a common problem of the fixed point problem and the quasimonotone variational inequality problem in Hilbert spaces. We propose an iterative algorithm to find a common element of the solution of a quasimonotone variational inequality and the fixed point of a pseudocontractive operator. Convergence theorems are proven under certain mild conditions, and several corollaries are obtained.