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A Unifying Approach to Variational Relation Problems

Author

Listed:
  • R. P. Agarwal

    (Texas A&M University, Kingsville)

  • M. Balaj

    (University of Oradea)

  • D. O’Regan

    (National University of Ireland)

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.

Suggested Citation

  • R. P. Agarwal & M. Balaj & D. O’Regan, 2012. "A Unifying Approach to Variational Relation Problems," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 417-429, November.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:2:d:10.1007_s10957-012-0090-x
    DOI: 10.1007/s10957-012-0090-x
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    References listed on IDEAS

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    7. S. H. Hou & H. Yu & G. Y. Chen, 2003. "On Vector Quasi-Equilibrium Problems with Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 119(3), pages 485-498, December.
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    1. M. Darabi & J. Zafarani, 2015. "Tykhonov Well-Posedness for Quasi-Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 458-479, May.
    2. Anulekha Dhara & Dinh Luc, 2014. "A solution method for linear variational relation problems," Journal of Global Optimization, Springer, vol. 59(4), pages 729-756, August.

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