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Generalized Variational Relation Problems with Applications

Author

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  • M. Balaj

    (University of Oradea)

  • L. J. Lin

    (National Changhua University of Education)

Abstract

In this paper, we first obtain an existence theorem of the solutions for a variational relation problem. An existence theorem for a variational inclusion problem, a KKM theorem and an extension of the well know Ky Fan inequality will be established, as particular cases. Some applications concerning a saddle point problem with constraints, existence of a common fixed point for two mappings and an optimization problem with constraints, will be given in the last section of the paper.

Suggested Citation

  • M. Balaj & L. J. Lin, 2011. "Generalized Variational Relation Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 1-13, January.
    • Handle: RePEc:spr:joptap:v:148:y:2011:i:1:d:10.1007_s10957-010-9741-y
    DOI: 10.1007/s10957-010-9741-y
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    References listed on IDEAS

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    1. D. T. Luc, 2008. "An Abstract Problem in Variational Analysis," Journal of Optimization Theory and Applications, Springer, vol. 138(1), pages 65-76, July.
    2. Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 233-245, December.
    3. Jun-Yi Fu, 2000. "Generalized vector quasi-equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(1), pages 57-64, September.
    4. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, September.
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    Cited by:

    1. R. P. Agarwal & M. Balaj & D. O’Regan, 2014. "A Common Fixed Point Theorem with Applications," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 482-490, November.
    2. Phan Khanh & Lai Lin & Vo Long, 2014. "On topological existence theorems and applications to optimization-related problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(3), pages 253-272, June.
    3. 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.
    4. 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.
    5. M. Balaj & L. J. Lin, 2013. "Existence Criteria for the Solutions of Two Types of Variational Relation Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 232-246, February.
    6. Zhe Yang & Yong Jian Pu, 2012. "Generalized Knaster–Kuratowski–Mazurkiewicz Theorem Without Convex Hull," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 17-29, July.
    7. Phan Khanh & Vo Long, 2014. "Invariant-point theorems and existence of solutions to optimization-related problems," Journal of Global Optimization, Springer, vol. 58(3), pages 545-564, March.

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