In this paper we deal with the following generalized vector variational inequality problem: let X, Y and Z be topological vector spaces, K be a convex set in X, D be a nonempty set in Y , and C be a closed convex cone in Z. Let T : K → 2 be a multifunction and f : K ×D ×K → Z be a single-valued mapping. Find a point x̂ ∈ K and ŷ ∈ T (x̂) such that f(x̂, ŷ, z) / ∈ −intC, ∀z ∈ K. We prove some exist...

In this communication, we establish some existence theorem for a new class of generalized mixed vector quasi-variationallike inequalities with fuzzy mappings in topological vector spaces by using the KKM-Fan Theorem and an equivalent fixed point theorem.

We apply the KKM technique to study generalized vector implicit variational inequality problem. Our results generalize the works of Huang and Li [8], Li and Huang [11], and represent variant of result of Lee and Farajzadeh [10]. We also obtain a version of best approximations theorem in cone metric spaces.

Abstract: In this paper, we generalize the (V, ρ)-invexity defined for nonsmooth multiobjective fractional programming by Mishra, Rueda and Giorgi (2003) to variational programming problems by defining new classes of vector-valued functions called (V, ρ)B-type I and generalized (V, ρ)-B-type I. Then we use these new classes to derive various sufficient optimality conditions and mixed type duali...

The purpose of this paper is to establish some relationships between proper efficiency of set-valued optimization problems and proper efficiency of vector variational-like inequalities under the assumptions of generalized cone-preinvexity. Our results extend and improve the corresponding results in the literature.

A general vector-valued variational inequality (GVVO is considered. We establish the existence theorem for (GVVI) in the noncompact setting, which is a noncompact generalization of the existence theorem for (GVVI) obtained by Lee et al., by using the generalized form ofKKM theorem due to Park. Moreover, we obtain the fiu2y extension ofour existence theorem.

Uniqueness and regularity results for local vector-valued generalized minimizers and for local stress tensors associated to variational problems with linear growth conditions are established. Assuming that the energy density f has the structure f(Z) = h(|Z|), only very weak ellipticity assumptions are required. For the proof we combine arguments from measure theory and convex analysis with the ...

We present new necessary optimality conditions for εe–Pareto optimal solutions of constrained vector optimization problems with empty interior ordering cones. We use the dual-space approach based on advanced tools of variational analysis and generalized differentiation. It allows us not implement any scalarization technique while be able to establish necessary results for nonconvex and nonsolid...

In this paper, we consider the variational homotopy perturbation method (VHPM) to obtain an approximate series solution for the generalized Fisher’s equation which converges to the exact solution in the region of convergence. Comparisons are made among the variational iteration method (VIM), the exact solutions and the proposed method. The results reveal that the proposed method is very effectiv...