In this paper, the concepts of well-posednesses and Hadamard well-posedness for a family of mixed variational inequalities are studied. Also, some metric characterizations of them are presented and some relations between well-posedness and Hadamard well-posedness of a family of mixed variational inequalities is studied. Finally, a relation between well-posedness for the family of mixed variatio...

We show the validity of select existence results for a vector optimization problem, and a variational inequality. More generally, we consider generalized vector quasi-variational inequalities, as well as, fixed point problems on genuine Hadamard manifolds.

It is well known that equilibrium problems are very important mathematical models and are closely related with fixed point problems, variational inequalities, and Nash equilibrium problems. Gap functions and error bounds which play a vital role in algorithms design, are two much-addressed topics of vector equilibrium problems. This paper is devoted to studying the scalar-valued gap functions an...

we introduce variational inequality problems on hilbert $c^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. then relation between variational inequalities, $c^*$-valued metric projection and fixed point theory  on  hilbert $c^*$-modules is studied.

In this paper, we consider the system of vector quasi-equilibrium problems with or without involving -condensing maps and prove the existence of its solution. Consequently, we get existence results for a solution to the system of vector quasi-variational-like inequalities. We also prove the equivalence between the system of vector quasi-variational-like inequalities and the Debreu type equilibr...

In recent years, sequential optimality conditions are frequently used for convergence of iterative methods to solve nonlinear constrained optimization problems. The sequential optimality conditions do not require any of the constraint qualications. In this paper, We present the necessary sequential complementary approximate Karush Kuhn Tucker (CAKKT) condition for a point to be a solution of a ...

Solvabilities of generalized vector variational-type inequalities (GVVTI) are discussed in this work. First, the solvability of GVVTI without monotone assumption for mappings is considered in (reflexive) Banach spaces by using Brouwer fixed point theorem (Browder fixed point theorem). Second, the solvability of GVVTI with monotone assumption for mappings is considered in reflexive Banach spaces...

The aim of this paper is to show connections between the sensitivity of the solutions of variational inequalitites and properties of the solution sets of vector variational inequalities in the infinite dimensional setting. We will show that, in some cases, the solution set of a vector variational inequality is a bijective and continuous image of a connected subset of the surface of the unit bal...

We consider vector variational inequalities defined by means of the usual componentwise ordering in a finite dimensional Euclidean space. Our principal result shows that, under suitable convexity assumptions, every weak solution of a vector variational inequality is a strong solution of a reduced variational inequality, obtained from the initial one by considering a selection of components.