On a class of fuzzy parametric variational inequality controlled differential equation problems in finite dimension spaces
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This work is motivated by the fact that very little is known about the fuzzy variational inequalities controlled differential equation problems in finite dimension real numeral spaces, which are studied more difficult than differential variational inequalities. It is interesting and challenging that how to solve the fuzzy variational inequalities in a fuzzy environment. The purpose of this paper is to introduce and study a class of new fuzzy parametric variational inequality controlled initial-value differential equation problems in finite dimensional Euclidean spaces. We establish existence of Carathéodory weak solutions for the fuzzy parametric variational inequality controlled initial-value differential equation problem under suitable conditions. Further, using method of centres with entropic regularization techniques and time-stepping methods, we emerge convergence analysis on iterative process for solving the initial-value differential fuzzy parametric inequalities. Finally, we give some open questions for our future research.
KeywordsFuzzy variational inequalities controlled differential equation Existence of Carathéodory weak solution Method of centres with entropic regularization techniques Time-stepping method Convergence analysis
Mathematics Subject Classification49J40 65K05 90C30 90C33
This work has been partially supported by the Science and Technology Plan Projects of Sichuan Province (2017JY0125), and the Scientific Research Project of Sichuan University of Science and Engineering (2017RCL54, 2013PY07).
- Hu, C. F. (1997). Solving systems of fuzzy inequalities. Ph.D. Thesis, North Carolina State University.Google Scholar
- Lan, H. Y., Liu, C. J., & Lu, T. X. (2013). Method of centres for solving mathematical programs with fuzzy parametric variational inequality constraints. In X. S. Zhang et al. (Ed.), 11th International Symposium on Operations Research and its Applications in Engineering, Technology and Management (Vol. 2013, No. 644CP, pp. 194–199). Stevenage: The Institution of Engineering and Technology.Google Scholar
- Li, W., Wang, X., & Huang, N. J. (2014). A system of differential set-valued variational inequalities in finite dimensional spaces. Journal of Function Spaces, 2014, 918796.Google Scholar