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Projection iterative methods for extended general variational inequalities

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Abstract

In this paper, we introduce and study a new class of variational inequalities involving three operators, which is called the extended general variational inequality. Using the projection technique, we show that the extended general variational inequalities are equivalent to the fixed point and the extended general Wiener-Hopf equations. This equivalent formulation is used to suggest and analyze a number of projection iterative methods for solving the extended general variational inequalities. We also consider the convergence of these new methods under some suitable conditions. Since the extended general variational inequalities include general variational inequalities and related optimization problems as special cases, results proved in this paper continue to hold for these problems.

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Authors and Affiliations

  1. Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan

    Muhammad Aslam Noor

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  1. Muhammad Aslam Noor
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Correspondence to Muhammad Aslam Noor.

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Noor, M.A. Projection iterative methods for extended general variational inequalities. J. Appl. Math. Comput. 32, 83–95 (2010). https://doi.org/10.1007/s12190-009-0234-9

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  • DOI: https://doi.org/10.1007/s12190-009-0234-9

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