MathLAB Journal

Approximation of solutions of monotone variational inequality problems with applications in real Hilbert spaces

Abstract

E. U. Ofoedu, C. B. Osigwe, K. O. Ibeh, G. C. Ezeamama

In this paper, variational inequality problem related to monotone operators is studied, and an iterative algorithm
which is a modication of extragradient method is proposed for approximation of solution (assuming existence) of the
variational inequality problem. Weak and strong convergence theorems are obtained and as applications, the iterative
scheme proposed is shown to also approximate xed points of pseudocontractive mappings, zeros of monotone mappings
and solutions of equilibrium problems. A numerical example is given to show the functionality of the studied scheme.
The obtained results improve and unify the corresponding results of several authors.<