A Class Of Random Generalized Set-Valued Strongly Nonlinear Implicit Quasi-Variational Inequlities

It is well-known that the theory of variational inequalities is an important branch of mathematics and has many important application in theoretical and applied science in the past two hundred years. In those years, the variational inequalities are applied to solve some problem arisen in applied mathematics, physics, nonlinear program, economics, finance and transport fields. Not long ago, A.Nagurney discussed a series of financial problems that based on variational inequalities. This is a wider and better use of variational inequalities theory. In this paper, we discuss spatial price equilibrium model with ad valorem tariffs which can be formulated into a variational inequality problem (complementarity problem) oIn this paper, we introduce and study a new class of random generalized set-valued strongly nonlinear implicit quasi-varational inequalities problem which includes many kinds of variational inequalities and quasi-inequalities as special cases 0 Using random theory of random bounded linear function and the property of the project operator, we transform this problem into a problem of random mapping fixed point. By Nadler lemma, we construct a new iterative random algorithm of the approximation solvability of this problem. On the condition ,we prove the existence of solution for this class of random generalized set-valued strongly nonlinear implicit quasi-variational inequalities problem and the convergence of sequence generalized by algorithm. These works improve and develop some recent main results of some authors.