On the existence problem of solutions to a class of fuzzy mixed exponential vector variational inequalities

Volume 11, Issue 7, pp 916--926 http://dx.doi.org/10.22436/jnsa.011.07.04

Publication Date: May 17, 2018 Submission Date: October 18, 2017 Revision Date: December 01, 2017 Accteptance Date: December 09, 2017

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 2021 Downloads
• 4192 Views

Authors

Shih-Sen Chang - Center for General Education, China Medical University, Taichung 40402, Taiwan. S. Salahuddin - Department of Mathematics, Jazan University, Jazan, Kingdom of Saudi Arabia. Ching-Feng Wen - Center for Fundamental Science; and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 80708, Taiwan. - Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 80708, Taiwan. Xiong Rui Wang - Department of Mathematics, Yibin University, Yibin, Sichuan 644007, China.

Abstract

In this research article, we deal with a new kind of mixed exponential fuzzy vector variational inequalities in ordered Euclidean spaces. By using KKM-technique and Nadler's fixed point theorem, we prove some existence theorems of solutions to mixed exponential vector variational inequality problems in fuzzy environment.

Share and Cite

Keywords

• Mixed exponential vector variational inequality problems
• fuzzy mappings
• fuzzy upper and lower semicontinuous mappings
• \(\alpha_g\)-relaxed exponentially \((\gamma,\eta)\)-monotone mapping
• KKM-mappings
• Nadler's fixed points theorem
• ordered Euclidean spaces

MSC

•  47H09
•  47J20

References

• [1] M. K. Ahmad, S. Salahuddin, A fuzzy extension of generalized implicit vector variational like inequalities, Positivity, 11 (2007), 477–484.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [2] M. K. Ahmad, S. Salahuddin , Existence of solution for generalized implicit vector variational like inequalities, Nonlinear Anal., 67 (2007), 430–441.
  • View Article
  • MathSciNet
  • Google Scholar


• [3] M. K. Ahmad, S. Salahuddin, Fuzzy generalized variational like inequality problems in topological vector spaces, J. Fuzzy Set Valued Anal., 2013 (2013), 5 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] G. A. Anastassiou, S. Salahuddin, Weakly set valued generalized vector variational inequalities, J. Comput. Anal. Appl., 15 (2013), 622–632.
  • MathSciNet
  • Google Scholar
  • MATH


• [5] L. Q. Anh, P. Q. Khanh, Existence conditions in symmetric multivalued vector quasiequilibrium problems, Control Cybernet., 36 (2007), 519–530.
  • MathSciNet
  • Google Scholar
  • MATH


• [6] L. E. J. Brouwer, Zur invarianz des n-dimensional gebietes, Math. Ann., 71 (1912), 305–313.
  • Google Scholar


• [7] L. C. Ceng, J. C. Yao , On generalized variational-like inequalities with generalized monotone multivalued mappings, Appl. Math. Lett., 22 (2009), 428–434.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182–190.
  • View Article
  • Google Scholar


• [9] S. S. Chang, S. Salahuddin , Existence of vector quasi variational like inequalities for fuzzy mappings, Fuzzy Sets and Systems, 233 (2013), 89–95.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] S. S. Chang, S. Salahuddin, M. K. Ahmad, X. R. Wang, Generalized vector variational like inequalities in fuzzy environment, Fuzzy Sets and System, 265 (2015), 110–120.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [11] S.-S. Chang, Y.-G. Zhu, On variational inequalities for fuzzy mappings, Fuzzy Sets and Systems, 32 (1989), 359–367.
  • View Article
  • MathSciNet
  • Google Scholar


• [12] G. Y. Chen, Existence of solutions for a vector variational inequalities: An extension of Hartman-Stampacchia theorems, J. Optim. Theory Appl., 74 (1992), 445–456.
  • View Article
  • Google Scholar


• [13] G.-Y. Chen, G.-M. Cheng, Vector variational inequality and vector optimizations problem, Toward Interactive and Intelligent Decision Support Systems, Lecture Notes in Economics and Mathematical Systems, Springer, Berlin, Heidelberg (1987)
  • View Article
  • Google Scholar


• [14] Y. J. Cho, S. Salahuddin, M. K. Ahmad, A fuzzy extension of generalized vector version of Minty lemma and applications, J. Fuzzy Maths., 15 (2007), 449–458.
  • MathSciNet
  • Google Scholar
  • MATH


• [15] X. P. Ding, S. Salahuddin, Fuzzy generalized mixed vector quasi variational like inequalities, J. Emerging Trends Comput. Information Sci., 4 (2013), 881–887.
  • Google Scholar


• [16] X. P. Ding, S. Salahuddin, M. K. Ahmad, Fuzzy generalized vector variational inequalities and complementarity problems, Nonlinear Funct. Anal. Appl., 13 (2008), 253–263.
  • MathSciNet
  • MATH


• [17] K. Fan, A generalization of tychonoff’s fixed point theorem, Math. Ann., 142 (1961), 305–310.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [18] Y. P. Fang, N. J. Huang, Variational-like inequalities with generalized monotone mappings in Banach spaces, J. Optim. Theory Appl., 118 (2003), 327–338.
  • View Article
  • MathSciNet
  • Google Scholar


• [19] F. Giannessi , Theorems of the Alternative, Quadratic Programs, and Complementarity Problems, Variational Inequalities and Complementarity Problems, Edited by R. W. Cottle, F. Giannessi, and J. L. Lions, John Wiley and Sons, New York (1980)
  • Google Scholar
  • MATH


• [20] N.-J. Huang, C.-J. Gao, Some generalized vector variational inequalities and complementarity problems for multivalued mappings, Appl. Math. Lett., 16 (2003), 1003–1010.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [21] A. Jayswal, S. Choudhury, R. U. Verma , Exponential type vector variational-like inequalities and vector optimization problems with exponential type invexities, J. Appl. Math. Comput., 45 (2014), 87–97.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [22] P. Q. Khanh, N. H. Quan , Generic stability and essential components of generalized KKM points and applications, J. Optim. Theory Appl., 148 (2011), 488–504.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [23] B. S. Lee, S. Salahuddin, A hemivariational-like inequality with applications, J. Nonlinear Convex Anal., 16 (2015), 141–150.
  • MathSciNet
  • Google Scholar
  • MATH


• [24] B. S. Lee, S. Salahuddin , Minty lemma for inverted vector variational inequalities, Optimization, 66 (2017), 351–359.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [25] K. L. Lin, D.-P. Yang, J. C. Yao, Generalized vector variational inequalities, J. Optim. Theory Appl., 92 (1997), 117–125.
  • View Article
  • Google Scholar


• [26] S. B. J. Nadler , Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475–488.
  • MathSciNet
  • Google Scholar
  • MATH


• [27] S. Salahuddin, M. K. Ahmad, R. U. Verma , Existence theorem for fuzzy mixed vector F-variational inequalities, Adv. Nonlinear Var. Inequal., 16 (2013), 53–59.
  • MathSciNet
  • Google Scholar
  • MATH


• [28] S. Salahuddin, B. S. Lee, Fuzzy general nonlinear ordered random variational inequalities in ordered Banach spaces , East Asian Math. J., 32 (2016), 685–700.
  • View Article
  • Google Scholar
  • MATH


• [29] S. Salahuddin, R. U. Verma, A common fixed point theorem for fuzzy mappings, Trans. Math. Prog. Appls., 1 (2013), 59–68.
  • Google Scholar


• [30] A. H. Siddiqi, M. F. Khan, S. Salahuddin, On vector variational like inequalities, Far East J. Math. Sci., Special Volume, Part III, (1998), 319–329.
  • MathSciNet


• [31] K.-Q. Wu, N.-J. Huang, Vector variational-like inequalities with relaxed \(\eta-\alpha\)-Pseudomonotone mappings in Banach spaces, J. Math. Inequal., 1 (2007), 281–290.
  • View Article
  • Google Scholar
  • MATH


• [32] L. A. Zadeh, Fuzzy sets, Information Control, 8 (1964), 338–353.
  • View Article
  • Google Scholar