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Resolvent Methods for Solving System of General Variational Inclusions

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Abstract

In this paper, we introduce and consider some new systems of extended general variational inclusions involving seven different operators. Using the resolvent operator technique, we show that the new systems of extended general variational inclusions are equivalent to the fixed point problems. This equivalent formulation is used to suggest and analyze some new iterative methods for this system of extended general variational inclusions. We also study the convergence analysis of the new iterative method under certain mild conditions. Several special cases are also discussed. Results obtained in this paper can be viewed as pure mathematical contribution to variational analysis.

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Authors and Affiliations

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

    M. A. Noor & K. I. Noor

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

    M. A. Noor

Authors
  1. M. A. Noor
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  2. K. I. Noor
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Correspondence to M. A. Noor.

Additional information

Communicated by R. Glowinski.

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Noor, M.A., Noor, K.I. Resolvent Methods for Solving System of General Variational Inclusions. J Optim Theory Appl 148, 422–430 (2011). https://doi.org/10.1007/s10957-010-9751-9

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  • DOI: https://doi.org/10.1007/s10957-010-9751-9

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