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A Unifying Approach to Variational Relation Problems

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Abstract

The purpose of this paper is to present a unified approach to study the existence of solutions for two types of variational relation problems, which encompass several generalized equilibrium problems, variational inequalities and variational inclusions investigated in the recent literature. By using two well-known fixed point theorems, we establish several existence criteria for the solutions of these problems.

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Acknowledgements

The authors thank the anonymous referee for his suggestions which have improved the presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, Kingsville, 700 University Blvd., Kingsville, TX, 78363-8202, USA

    R. P. Agarwal

  2. Department of Mathematics, University of Oradea, 410087, Oradea, Romania

    M. Balaj

  3. Department of Mathematics, National University of Ireland, Galway, Ireland

    D. O’Regan

Authors
  1. R. P. Agarwal
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  2. M. Balaj
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  3. D. O’Regan
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Corresponding author

Correspondence to R. P. Agarwal.

Additional information

Communicated by Lionel Thibault.

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Agarwal, R.P., Balaj, M. & O’Regan, D. A Unifying Approach to Variational Relation Problems. J Optim Theory Appl 155, 417–429 (2012). https://doi.org/10.1007/s10957-012-0090-x

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  • DOI: https://doi.org/10.1007/s10957-012-0090-x

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