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Solution of a class of equilibrium problems and variational inequalities in FC spaces

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  • Gayatri Pany

    (IIT)

  • Ram N. Mohapatra

    (University of Central Florida)

  • Sabyasachi Pani

    (IIT)

Abstract

In this paper, we study a class of mixed variational-like inequalities with respect to generalized weakly relaxed $$\eta {-}\alpha $$ η - α monotone mappings, involving nonlinear bifunctions, in finitely continuous topological space, in short FC space. Existence of the solution to the problem is established relaxing convexity and linearity condition by using generalized RKKM theorem. We have proposed a proximal iterative scheme using auxiliary principle technique. Solvability of the auxiliary variational inequality problem is established. Finally convergence of the iterates to the exact solution is proved. Some results with application to equilibrium problem are also discussed.

Suggested Citation

  • Gayatri Pany & Ram N. Mohapatra & Sabyasachi Pani, 2018. "Solution of a class of equilibrium problems and variational inequalities in FC spaces," Annals of Operations Research, Springer, vol. 269(1), pages 565-582, October.
    • Handle: RePEc:spr:annopr:v:269:y:2018:i:1:d:10.1007_s10479-017-2506-3
    DOI: 10.1007/s10479-017-2506-3
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    References listed on IDEAS

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    1. Farajzadeh, A.P. & Plubtieng, S. & Ungchittrakool, K. & Kumtaeng, D., 2015. "Generalized mixed equilibrium problems with generalized α -η -monotone bifunction in topological vector spaces," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 313-319.
    2. Guoqiang Tian, 1993. "Generalized Quasi-Variational-Like Inequality Problem," Mathematics of Operations Research, INFORMS, vol. 18(3), pages 752-764, August.
    3. Xie Ding, 2012. "Equilibrium existence theorems for multi-leader-follower generalized multiobjective games in FC-spaces," Journal of Global Optimization, Springer, vol. 53(3), pages 381-390, July.
    4. Ouayl Chadli & Qamrul Hasan Ansari & Suliman Al-Homidan, 2017. "Existence of Solutions and Algorithms for Bilevel Vector Equilibrium Problems: An Auxiliary Principle Technique," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 726-758, March.
    5. Ben-El-Mechaiekh, H. & Chebbi, S. & Florenzano, M. & Llinares, J.-V., 1997. "Abstract Convexity and Fixed Points," Papiers d'Economie Mathématique et Applications 97.87, Université Panthéon-Sorbonne (Paris 1).
    6. Y.P. Fang & N.J. Huang, 2003. "Variational-Like Inequalities with Generalized Monotone Mappings in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 327-338, August.
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    Cited by:

    1. G. C. Bento & J. X. Cruz Neto & P. A. Soares & A. Soubeyran, 2022. "A new regularization of equilibrium problems on Hadamard manifolds: applications to theories of desires," Annals of Operations Research, Springer, vol. 316(2), pages 1301-1318, September.

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