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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


Fuzzy (η,ϕ)-mixed Vector Equilibrium Problems

Discontinuity, Nonlinearity, and Complexity 8(3) (2019) 271--277 | DOI:10.5890/DNC.2019.09.003

Salahuddin

Department of Mathematics, Jazan University, Jazan, Kingdom of Saudi Arabia

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Abstract

In this research document, we study the fuzzy (η,ϕ)-mixed vector equilibrium problems. By using the concepts of KKM-mapping, we prove the existence theorem of fuzzy (η,ϕ)-mixed vector equilibrium problems.

References

  1. [1]  Zadeh, L.A., (1964), Fuzzy sets, Information Control, 8, 338-353.
  2. [2]  Chang, S.S. and Tan, K.K., (2002), Equilibria and maximal elements of abstract fuzzy economics and qualitative fuzzy games, Fuzzy Sets Systems, 125, 389-399.
  3. [3]  Chang, S.S. and Huang, N.J., (1993), Generalized complementarity problem for fuzzy mappings, Fuzzy Sets Systems, 55, 227-234.
  4. [4]  Khan, M.F., Husain, S., and Salahuddin (2008), A fuzzy extension of generalized multivalued η-mixed vector variational like inequalities on locally convex Hausdorff topology vector spaces, Bull. Cal. Math. Soc., 100(1), 27-36.
  5. [5]  Zimmermann, H.Z., (1988), Fuzzy Set Theory and its Applications, Kluwer Acad. Publ. Dordrecht.
  6. [6]  Chang, S.S. and Zhu, Y.G. (1989), On variational inequalities for fuzzy mappings, Fuzzy Sets Systems, 32, 359-367.
  7. [7]  Ahmad, M.K. and Salahuddin (2007), A fuzzy extension of generalized implicit vector variational like inequalities, Positivity, 11(3), 477-484.
  8. [8]  Ahmad, M.K. and Salahuddin (2012), Fuzzy generalized variational like inequality problems in topological vector spaces, J. Fuzzy Set Valued Anal., 2012, Article ID: jfsva-00134, (2012), page 7.
  9. [9]  Chang, S.S. and Salahuddin (2013), Existence of vector quasi variational like inequalities for fuzzy mappings, Fuzzy Sets Systems, 233, 89-95.
  10. [10]  Chang, S.S., Salahuddin, Ahmad, M.K., and Wang, X.R., (2015), Generalized vector variational like inequalities in fuzzy environment, Fuzzy Sets Systems, 265, 110-120.
  11. [11]  Cho, Y.J., Ahmad, M.K., and Salahuddin (2007), A fuzzy extension of generalized vector version of Mintys lemma and applications, The J. Fuzzy Maths., 15(2), 449-458.
  12. [12]  Ding, X.P., Ahmad, M.K., and Salahuddin, (2008), Fuzzy generalized vector variational inequalities and complementarity problems, Nonlinear Funct. Anal. Appl., 13(2), 253-263.
  13. [13]  Ding, X.P. and Salahuddin (2013), Fuzzy generalized mixed vector quasi variational like inequalities, J. Emerging Trends Comput. Information Sci., 4(11), 880-887.
  14. [14]  Lee, B.S. and Salahuddin (2016), Fuzzy general nonlinear ordered random variational inequalities in ordered Banach spaces, East Asian Math. J., 32(5), 685-700.
  15. [15]  Verma, R.U. and Salahuddin (2013), A common fixed point theorem for fuzzy mappings, Trans. Math. Prog. Appls., 1(1), 59-68.
  16. [16]  Verma, R.U., Ahmad, M.K., and Salahuddin (2013), Existence theorem for fuzzy mixed vector F-variational inequalities, Adv. Nonlinear Var. Inequal., 16(1), 53-59.
  17. [17]  Xiao, G., Fan, Z., and Qi, R., (2010), Existence results for generalized nonlenear vector variational like inequalities with set valued mapping, Appl. Math. Lett., 23, 44-47.
  18. [18]  Lee, G.M., Kim, D.S., and Lee, B.S. (1999), Vector variational inequality for fuzzy mappings, Nonlinear Anal Forum, 4, 119-129.
  19. [19]  Brouwer, L., (1912), Zur invarianz des n-dimensional gebietes, Math. Ann., 71(3), 305-313.
  20. [20]  Su, C.H. and Sehgal, V.M. (1975), Some fixed point theorems for condensing multifunctions in locally convex spaces, Proc. Natl. Acad. Sci. USA, 50, 150-154.
  21. [21]  Aubin, J.P. (2000), Applied Functional Analysis, John Wiley and Sons.
  22. [22]  Fan, K. (1972), A minimax inequality and its applications:In: O. Shisha(ed):Inequalities, vol. 3, pp.103-113, Academic Press, New York.
  23. [23]  Fan, K. (1961), A generalization of Tychonoff’s fixed point theorem, Math. Ann., 142, 305-310.