On a class of fuzzy parametric variational inequality controlled differential equation problems in finite dimension spaces

Abstract

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 Caratheodory 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.