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Generalized mixed equilibrium problems with generalized α -η -monotone bifunction in topological vector spaces

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  • Farajzadeh, A.P.
  • Plubtieng, S.
  • Ungchittrakool, K.
  • Kumtaeng, D.

Abstract

The purpose of this paper is to introduce a new class of the generalized mixed equilibrium problems with a new definition of the relaxed monotonicity for bi-functions in topological vector spaces. By employing the KKM technique and under some appropriate assumptions on the considering nonlinear mappings, we obtain the existence of a solution for the generalized mixed equilibrium problems with the new concept of the relaxed monotonicity and coercivity condition(in order to relax the compactness of the domains of the nonlinear mappings) in the setting of topological vector spaces. Moreover, the compactness and convexness of the solution set are investigated. The results in the paper extend and generalize the corresponding results, especially Sintunavarat (2013) [20] in this area by providing mild assumptions in order to guarantee the existence of a solution for the generalized mixed equilibrium problem.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:313-319
    DOI: 10.1016/j.amc.2015.05.013
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    References listed on IDEAS

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    1. Monica Bianchi & Siegfried Schaible, 2004. "Equilibrium Problems under Generalized Convexity and Generalized Monotonicity," Journal of Global Optimization, Springer, vol. 30(2), pages 121-134, November.
    2. Yao, Yonghong & Cho, Yeol Je & Liou, Yeong-Cheng, 2011. "Algorithms of common solutions for variational inclusions, mixed equilibrium problems and fixed point problems," European Journal of Operational Research, Elsevier, vol. 212(2), pages 242-250, July.
    3. 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. 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.

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