A theorem for solving Banach generalized system of variational inequality problems and fixed point problem in uniformly convex and 2-uniformly smooth Banach space

Variational inequality over the set of common solutions of a system of bilevel variational inequality problem with applications

“…It is a useful mathematical model which unifies many important concepts in applied mathematics, such as necessary optimality conditions, network equilibrium problems, complementarity problems and systems of nonlinear equations, for instance [3,17,23,50]. Several iterative methods have been developed for solving variational inequalities and related optimization problems, see [10,11,[14][15][16]24,25] and the references therein. In particular, Korpelevich [26] presented the Extragradient method for solving variational inequalities with monotone and Lipschitz continuous mappings in Euclidean space.…”