Inertial Scheme for Solving Two-Level Variational Inequality and Fixed Point Problem Involving Pseudomonotone and ϱ — Demimetric Mappings

Abstract This work approximates the solution of two-level variational inequality and fixed point problem in a real Hilbert space where the underlying operators are pseudo-monotone and ϱ-demimetric. An iterative algorithm was developed and shown to converge strongly to the solution set of two-level variational inequality and fixed point problem. Four numerical examples are presented to further demonstrate the usefulness and applicability of our method. The result obtained extends, generalizes and compliments several existing results in this direction of research.