Wardrop [1] introduced the famous user equilibrium principle for traffic network, which is a scalar equilibrium principle. Smith [2] investigated that a Wardrop's user equilibrium flow is equivalent to the solution of a class of variational inequalities when the travel cost function is a scalar function. Recently, many researchers have proposed equilibrium models based on multicriteria consider...

In this article, our aim is to consider a class of fuzzy mixed variational-like inequalities (FMVLIs) for mapping known as extended perturbed (EPFMVLIs). As exceptional cases, some new and classically defined “FMVLIs” are also attained. We have studied the auxiliary principle technique “EPFMVLI” “EPFMVLI.” By using analytic results, existence results efficient numerical techniques established. ...

We establish the existence and uniqueness results for variational inequality problems on Riemannian manifolds and solve completely the open problem proposed in [21]. Also the relationships between the constrained optimization problem and the variational inequality problems as well as the projections on Riemannian manifolds are studied. Keyword: Variational inequalities; Riemannian manifold; Mon...

This paper proves the equilibrium existence for abstract economies with non-compact infinitedimensional strategy spaces, infinitely many agents, and discontinuous payolT (utility) functions by using the quasi-variational inequality approach. The motivations come from economic applications showing that payoff functions are discontinuous in many cases and the set of feasible allocations generally...

It is well known that the resolvent equations are equivalent to the extended general mixed variational inequalities. We use this alternative equivalent formulation to study the sensitivity of the extended general mixed variational inequalities without assuming the differentiability of the given data. Since the extended general mixed variational inequalities include extended general variational ...

In this paper, a class of generalized general mixed quasi variational inequalities is introduced and studied. We prove the existence of the solution of the auxiliary problem for the generalized general mixed quasi variational inequalities, suggest a predictor-corrector method for solving the generalized general mixed quasi variational inequalities by using the auxiliary principle technique. If ...

In this paper, we introduce a new class of bifunction variational inequalities, which is called the multivalued mixed quasi bifunction variational inequalities. Using the auxiliary principle technique, we suggest and analyze a proximal point method for solving the multivalued mixed quasi bifunction variational inequalities. It is shown that the convergence of the proposed method requires only p...

We introduce and study a new class of generalized nonlinear mixed variational-like inequalities in reflexive Banach spaces. By applying Ding’s technique we prove several existence and uniqueness theorems of solutions for the generalized nonlinear mixed variational-like inequality, extend the auxiliary problem technique to suggest and analyze an iterative method to compute the approximate soluti...