In this paper, we extend the concept of pseudomonotonicity from Rn to the setting of Euclidean Jordan algebras. We study interconnections between pseudomonotonicity, monotonicity, and the Z-property.

We present a new Bregman-function-based algorithm which is a modification of the generalized proximal point method for solving the variational inequality problem with a maximal monotone operator. The principal advantage of the presented algorithm is that it allows a more constructive error tolerance criterion in solving the proximal point subproblems. Furthermore, we eliminate the assumption of...

The purpose of this paper is to study the solvability for a class of generalized strong vector variational-like inequalities in reflexive Banach spaces. Firstly, utilizing Brouwer’s fixed point theorem, we prove the solvability for this class of generalized strong vector variational-like inequalities without monotonicity assumption under some quite mild conditions. Secondly, we introduce the ne...

In this paper, with the help of the duality operator and K. Fan’s lemma, we present existence results for strong vector equilibrium problems, under pseudomonotonicity assumptions and without any pseudomonotonicity assumptions, respectively. Then, as an application, the main results allow us to state existence theorems for strong vector variational inequality problems.

In this paper we propose a novel double projection recurrent neural network model for solving pseudomonotone variational inequalities based on a technique of updating the state variable and fixed point theorem. This model is stable in the sense of Lyapunov and globally convergent for problems that satisfy Lipschitz continuity and pseudomonotonicity conditions. The global exponential stability o...

In this paper, a strong version of Wald’s Axiom of excess demand functions Z : P ⊂ IR >0 → IR n is introduced, namely “there exists σ > 0 such that p, q ∈ P, qZ(p) − δ ≤ 0, |δ| < σ, and Z(q) 6= Z(p) imply pZ(q) + δ > 0”. We show that Z satisfies the strong version of Wald’s Axiom iff −Z is a s-quasimonotone function introduced in An (2006). Consequently, an excess demand function Z satisfies th...

The problems which imply variational inequality over product sets have many applications. Thus, the Nash equilibrium problem for differentiable functions, various equilibrium-type problems, as traffic equilibrium, spatial equilibrium and general equilibrium programming problems from economics, game theory, operations research, mathematical physics, for example, can be modelled as variational in...