An inertial scheme for solving bi-level variational inequalities and the fixed point problem with pseudomonotone and $\varrho$-demimetric mappings

Abstract

This paper investigates the solutions of a bi-level variational inequality problem and the fixed point problem of the operators, which are pseudo-monotone and ρ-demimetric in the framework of Hilbert spaces. An iterative scheme is presented and it is proved to be strongly convergent to the solution of the two problem. Four numerical examples are presented to demonstrate the usefulness and applicability of our scheme. The result obtained in this paper extends, generalizes, and compliments several existing results in this direction of this research.