Fuzzy (η,ϕ)-mixed Vector Equilibrium Problems
DOI:
https://doi.org/10.5890/DNC.2019.09.003Abstract
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] Zadeh, L.A., (1964), Fuzzy sets, Information Control, 8, 338-353.
[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] Chang, S.S. and Huang, N.J., (1993), Generalized complementarity problem for fuzzy mappings, Fuzzy Sets Systems, 55, 227-234.
[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] Zimmermann, H.Z., (1988), Fuzzy Set Theory and its Applications, Kluwer Acad. Publ. Dordrecht.
[6] Chang, S.S. and Zhu, Y.G. (1989), On variational inequalities for fuzzy mappings, Fuzzy Sets Systems, 32, 359-367.
[7] Ahmad, M.K. and Salahuddin (2007), A fuzzy extension of generalized implicit vector variational like inequalities, Positivity, 11(3), 477-484.
[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] Chang, S.S. and Salahuddin (2013), Existence of vector quasi variational like inequalities for fuzzy mappings, Fuzzy Sets Systems, 233, 89-95.
[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] 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] 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] 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] 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] Verma, R.U. and Salahuddin (2013), A common fixed point theorem for fuzzy mappings, Trans. Math. Prog. Appls., 1(1), 59-68.
[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] 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] Lee, G.M., Kim, D.S., and Lee, B.S. (1999), Vector variational inequality for fuzzy mappings, Nonlinear Anal Forum, 4, 119-129.
[19] Brouwer, L., (1912), Zur invarianz des n-dimensional gebietes, Math. Ann., 71(3), 305-313.
[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] Aubin, J.P. (2000), Applied Functional Analysis, John Wiley and Sons.
[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] Fan, K. (1961), A generalization of Tychonoff’s fixed point theorem, Math. Ann., 142, 305-310.
Article Metrics
Usage tracking begins September 1, 2026.