Qamrul Hasan Ansari

A fixed point theorem and its applications to a system of variational inequalities

In this paper, we first prove a fixed point theorem for a family of multivalued maps defined on product spaces. We then apply our result to prove an equilibrium existence theorem for an abstract economy. We also consider a system of variational inequalities and prove the existence of its solutions by using our fixed point theorem.

An existence result for the generalized vector equilibrium problem

Abstract In this paper, we prove an existence result for the generalized vector equilibrium problem by using Fan-Browder type fixed-point theorem due to [1].

System of vector equilibrium problems and its applications

In this paper, we introduce a system of vector equilibrium problems andprove the existence of a solution. As an application, we derive someexistence results for the system of vector variational inequalities. We alsoestablish some existence results for the system of vector optimizationproblems, which includes the Nash equilibrium problem as a special case.

A Generalization of Vectorial Equilibria

A generalized form of vectorial equilibria is proposed, and, using an abstract monotonicity condition, an existence result is demonstrated.

The system of generalized vector equilibrium problems with applications

In this paper, we introduce the system of generalized vector equilibrium problems which includes as special cases the system of generalized implicit vector variational inequality problems, the system of generalized vector variational and variational-like inequality problems and the system of vector equilibrium problems. By using a maximal element theorem, we establish existence results for a solution of these systems. As an application, we derive existence results for a solution of a more general Nash equilibrium problem for vector-valued functions.

Interative schemes for solving mixed variational-like inequalites 1,2

In the present paper, we introduce the concept of η-cocoercivity of a map and develop some iterative schemes for finding the approximate solutions of mixed variational-like inequalities. We use the concept of η-cocoercivity to prove the convergence of the approximate solutions to the exact solution of mixed variational-like inequalities.

Existence of a solution and variational principles for vector equilibrium problems

In this paper, we prove an existence result for a solution to the vector equilibrium problems. Then, we establish variational principles, that is, vector optimization formulations of set-valued maps for vector equilibrium problems. A perturbation function

Strongly nonlinear quasivariational inequalities

Abstract In this paper, we develop the algorithms for finding the approximate solution of a strongly nonlinear quasivariational inequality and a strongly nonlinear quasicomplementarity problem and we include as special cases known results in this area. We also observe that these two problems are equivalent if the convex set involved in the formulation of these problem is a convex cone.

General strongly nonlinear variational inequalities

Abstract In this paper we develop iterative algorithms for finding approximate solutions for new classes of variational and quasivariational inequalities which include, as a special case, some known results in this field. It is shown that the solutions of the iterative schemes converge to the exact solutions.

Characterization of solutions for vector equilibrium problems

In this paper, we characterize the solutions of vector equilibrium problems as well as dual vector equilibrium problems. We establish also vector optimization problem formulations of set-valued maps for vector equilibrium problems and dual vector equilibrium problems, which include vector variational inequality problems and vector complementarity problems. The set-valued maps involved in our formulations depend on the data of the vector equilibrium problems, but not on their solution sets. We prove also that the solution sets of our vector optimization problems of set-valued maps contain or coincide with the solution sets of the vector equilibrium problems.