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...

In this paper we consider the problem of finding an equilibrium in an economy with nonlinear constant returns to scale production activities. To find an equilibrium we propose an adjustment process in which the prices of the commodities and the activity levels of production adjust simultaneously. The process starts at a price vector at which each production activity has non positive profit. We ...

This Working Paper should not be reported as representing the views of the IMF. The views expressed in this Working Paper are those of the author(s) and do not necessarily represent those of the IMF or IMF policy. Working Papers describe research in progress by the author(s) and are published to elicit comments and to further debate. Recent turmoil in financial and commodities markets has renew...

In this paper, by using the famous Brouwer fixed point theorem, some existence theorems of strong efficient solutions for the strong vector equilibrium problems are obtained on noncompact sets of general real Hausdorff topological vector spaces without assuming that the dual of the ordering cone has a weak∗ compact base. Moreover, the closeness and the convexity of the strong efficient solution...

In this paper we study the solvability of a system of vector equilibrium problems. We extend the concept of topological pseudomonotonicity to a family of mappings. We prove existence results for the system of vector equilibrium problems under topological pseudomonotonicity conditions by the Kakutani-Fan-Glicksberg fixed point theorem. As applications, we obtain existence results for systems of ...

We consider lexicographic vector equilibrium problems in metric spaces. Sufficient conditions for a family of such problems to be (uniquely) well-posed at the reference point are established. As an application, we derive several results on well-posedness for a class of variational inequalities.

This paper presents some fundamental results about sufficient linear weighted complementarity problems. Such a problem depends on a nonnegative weight vector. If the weight vector is zero, the problem reduces to a sufficient linear complementarity problem that has been extensively studied. The introduction of the more general notion of a weighted complementarity problem (wCP) was motivated the ...

In this paper, we study Levitin-Polyak well-posedness for vector equilibrium problems with functional constraints. Two sufficient conditions of (generalized) Levitin-Polyak well-posedness are derived for vector equilibrium problems.