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Iterative methods for solving general quasi-variational inequalities

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Abstract

In this paper, we introduce a new class of variational inequalities, which is called the general quasi-variational inequality. We establish the equivalence among the general quasi variational inequality and implicit fixed point problems and the Wiener–Hopf equations. We use this equivalent formulation to discuss the existence of a solution of the general quasi-variational inequality. This equivalent formulation is used to suggest and analyze some iterative algorithms for solving the general quasi-variational inequality. We also discuss the convergence analysis of these iterative methods. Several special cases are also discussed.

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Authors and Affiliations

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

    Muhammad Aslam Noor & Khalida Inayat Noor

  2. Mathematics Department, College of Science, King Saud University, Riyadh, Saudi Arabia

    Muhammad Aslam Noor & Eisa Al-Said

Authors
  1. Muhammad Aslam Noor
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  2. Khalida Inayat Noor
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  3. Eisa Al-Said
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Correspondence to Muhammad Aslam Noor.

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Noor, M.A., Noor, K.I. & Al-Said, E. Iterative methods for solving general quasi-variational inequalities. Optim Lett 4, 513–530 (2010). https://doi.org/10.1007/s11590-010-0180-3

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  • DOI: https://doi.org/10.1007/s11590-010-0180-3

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