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.

Throughout this paper, let Z, E, and F be topological vector spaces, let X ⊆ E and Y ⊆ F be nonempty, closed, and convex subsets. Let D : X → 2X , T : X → 2Y and Ψ : X ×Y × X → 2Z be set-valued mappings, and let C : X → 2Z be a set-valued mapping such that C(x) is a closed pointed and convex cone with intC(x) = ∅ for each x ∈ X , where intC(x) denotes the interior of the set C(x). Then the gene...

In this paper, we introduce and study a generalized class of vector implicit quasi complementarity problem and the corresponding vector implicit quasi variational inequality problem. By using Fan-KKM theorem, we derive existence of solutions of generalized vector implicit quasi variational inequalities without any monotonicity assumption and establish the equivalence between those problems in B...

We consider a generalized ε-vector equilibrium problem which contain vector equilibrium problems and vector variational inequalities as special cases. By using the KKM theorem,we obtain some existence theorems for the generalized ε-vector equilibrium problem. We also investigate the duality of this generalized ε-vector equilibrium problem and discuss the equivalence relation between solutions o...

The purpose of this article was to establish manifold versions existence theorems for generalized vector quasi-equilibrium problems in locally compact and σ-compact spaces without any continuity assumption. fixed-point theorem a product Hadamard is the key focus our discussion. We further applied saddle point minimax problems.