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Volume 2, Issue 1
Volume 1, Issue 1

Some new iterative methods for solving variational inequalities

Pages: 1 – 17


M. A. Noor, K. I. Noor and A. Bnouhachem


Variational inequalities can be viewed as novel and significant extension of variational principles. A wide class of unrelated problems, which arise in various branches of pure and applied sciences are being investigated in the unified framework of variational inequalities. It is well known that variational inequalities are equivalent to the fixed point problems. This equivalent fixed point formulation has played not only a crucial part in studying the qualitative behavior of complicated problems, but also provide us numerical techniques for finding the approximate solution of these problems. Our main focus is to suggest some new iterative methods for solving variational inequalities and related optimization problems using projection methods, Wiener-Hopf equations and dynamical systems coupled with finite difference technique. Convergence analysis of these methods is investigated under suitable conditions. Some numerical examples are given to illustrate the efficiency of the proposed methods for solving variational inequalities.

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Received: 29 May 2020; Accepted: 24 June 2020.