This paper deals with the characterization of solutions for vector equilibrium problems by means of conjugate duality. By using the Fenchel duality we establish variational principles, that is, optimization problems with set-valued objective functions, the solution sets of which contain the ones of the vector equilibrium problems. The set-valued objective mappings depend on the data, but not on...

In this paper, we introduce the concept of ( ) x c h − -pseudomonotonicity. By considering the existence of solutions for the generalized vector equilibrium problems with a continuous selection theorem, we obtain some existence results for the generalized vector equilibrium problems with point-to-set mappings.

The Muttalib–Borodin biorthogonal ensemble is a joint density function for n particles on the positive real line that depends on a parameter θ. There is an equilibrium problem that describes the large n behavior. We show that for rational values of θ there is an equivalent vector equilibrium problem.

(1) x0 ∈ K such that c1 ≤ f(x0, y) ≤ c2, for all y ∈ K, where K is a given set, f : K × K → R is a given function and c1 and c2 two real numbers such that c1 ≤ c2. If K is a nonempty closed subset in a locally convex semi-reflexive topological vector space, then the problem (1) is problem by Isac, Sehgal and Singh [16] (Open Problem 2). In [20], Li gave the answer of this problem by introducing...

Traffic network equilibrium problems with capacity constraints of arcs are studied. A weak vector equilibrium principle with vector-valued cost functions, which are different from the ones in the work of Lin 2010 , and three kinds of parametric equilibrium flows are introduced. Some necessary and sufficient conditions for a weak vector equilibrium flow to be a parametric equilibrium flow are de...

The aim of this work is to analyze lexicographic equilibrium problems on a topological Hausdorff vector space X, and their relationship with some other vector equilibrium problems. Existence results for the tangled lexicographic problem are proved via the study of a related sequential problem. This approach was already followed by the same authors in the case of variational inequalities.

In this paper, a new form of the symmetric vector equilibrium problem is introduced and, by mixing properties of the nonlinear scalarization mapping and the maximal element lemma, an existence theorem for it is established. We show that Ky Fan's lemma, as a usual technique for proving the existence results for equilibrium problems, implies the maximal element lemma, while it is useless for prov...

we prove a strong convergence result for a sequence generated by halpern's type iteration for approximating a common fixed point of a countable family of quasi-lipschitzian mappings in a real hilbert space. consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...