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On certain classes of variational inequalities and related iterative algorithms

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  • Muhammad Aslam Noor

Abstract

In this paper, we introduce and study some new classes of variational inequalities and Wiener-Hopf equations. Essentially using the projection technique, we establish the equivalence between the multivalued general quasi-variational inequalities and the multivalued implicit Wiener-Hopf equations. This equivalence enables us to suggest and analyze a number of iterative algorithms for solving multivalued general quasi-variational inequalities. We also consider the auxiliary principle technique to prove the existence of a unique solution of the variational-like inequalities. This technique is used to suggest a general and unified iterative algorithm for computing the approximate solution. Several special cases which can be obtained from our main results are also discussed. The results proved in this paper represent a significant refinement and improvement of the previously known results.

Suggested Citation

  • Muhammad Aslam Noor, 1996. "On certain classes of variational inequalities and related iterative algorithms," International Journal of Stochastic Analysis, Hindawi, vol. 9, pages 1-14, January.
    • Handle: RePEc:hin:jnijsa:787061
    DOI: 10.1155/S1048953396000056
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