Implicit vector equilibrium problems with applications

Duality for vector equilibrium problems with constraints

‎In the paper‎, ‎we study duality for vector equilibrium problems using a concept of generalized convexity in dealing with the quasi-relative interior‎. ‎Then‎, ‎their applications to optimality conditions for quasi-relative efficient solutions are obtained‎. ‎Our results are extensions of several existing ones in the literature when the ordering cones in both the objective space and the constr...

Implicit Vector Equilibrium Problems via Nonlinear Scalarisation

The purpose of this paper is to introduce a nonlinear scalarisation function for solving a class of implicit vector equilibrium problems. We prove a scalarisation lemma to show the relation between the implicit vector equilibrium problem and the nonlinear scalarisation function. Then we derive some new existence theorems for solutions of implicit vector equilibrium problems, using the scalarisa...

On generalized implicit vector equilibrium problems in Banach spaces

Let X and Y be real Banach spaces, K be a nonempty convex subset of X , and C : K → 2Y be a multifunction such that for each u ∈ K , C(u) is a proper, closed and convex cone with intC(u) 6= ∅, where intC(u) denotes the interior of C(u). Given the mappings T : K → 2L(X,Y ,A : L(X, Y )→ L(X, Y ), f1 : L(X, Y )×K×K → Y , f2 : K×K → Y , and g : K → K , we introduce and consider the generalized impl...

On Generalized Implicit Vector Equilibrium Problems in Topological Ordered Spaces

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 so...