Approximation of Solutions of Monotone Variational Inequality Problems with Applications in Real Hilbert Spaces

  • Eric Uwadiegwu Ofoedu Department of Mathematics, Nnamdi Azikiwe University, Awka, Anambra State, Nigeria
  • Bona Chimezie Osigwe
  • Kingsley Obinna Ibeh
  • Genevieve Chinenye Ezeamama
Keywords: Fixed Point Problem, Hilbert Space, Monotone Mappings, Variational Inequality Problem, Approximation Method

Abstract

In this paper, variational inequality problem which hinges on operators of monotone type is studied, and an iterative algorithm which is a modification 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 fixed points of pseudocontractive mappings, zeros of monotone mappings and solutions of equilibrium problems. A numerical example is given to show the functionality of the scheme studied. The results obtained improve and unify the corresponding results of several authors.

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Published
2019-04-18
How to Cite
Ofoedu, E. U., Osigwe, B. C., Ibeh, K. O., & Ezeamama, G. C. (2019). Approximation of Solutions of Monotone Variational Inequality Problems with Applications in Real Hilbert Spaces. MathLAB Journal, 2(1), 17-34. Retrieved from http://purkh.com/index.php/mathlab/article/view/253
Section
Research Articles