In this paper, we study the mathematical program with equilibrium constraints (MPEC) formulated as a mathematical program with a parametric generalized equation involving the regular normal cone. Compared with the usual way of formulating MPEC through a KKT condition, this formulation has the advantage that it does not involve extra multipliers as new variables, and it usually requires weaker a...

We first consider an auxiliary problem for the generalized mixed vector equilibrium problem with a relaxed monotone mapping and prove the existence and uniqueness of the solution for the auxiliary problem. We then introduce a new iterative scheme for approximating a common element of the set of solutions of a generalized mixed vector equilibrium problem with a relaxed monotone mapping and the s...

Let A be an algebra, and let θ, φ be ring automorphisms of A. An additive mapping H : A → A is called a θ, φ -derivation if H xy H x θ y φ x H y for all x, y ∈ A. Moreover, an additive mapping F : A → A is said to be a generalized θ, φ -derivation if there exists a θ, φ derivation H : A → A such that F xy F x θ y φ x H y for all x, y ∈ A. In this paper, we investigate the superstability of gene...

In this paper, we introduce and consider a new class of complementarity problems, which are called the generalized mixed quasi-complementarity problems in a topological vector space. We show that the generalized mixed quasi-complementarity problems are equivalent to the generalized mixed quasi variational inequalities. Using a new type of KKM mapping theorem, we study the existence of a solutio...

In this paper, the generalized variational inequality with multi-valued mapping (GVI) is considered. To solve the problem, we first establish a global error bound estimation for GVI with the underlying multi-valued mapping being   strict monotone and Holder continuous. Based on this, we propose a new type of method to solve the GVI, and its global convergence is also established. Keywords-GVI...

We study infinite dimensional optimization problems where the constraint mapping is given as the sum of a smooth function and a generalized polyhedral multifunction, e.g. the normal cone mapping of a convex polyhedral set. By using advanced techniques of variational analysis we obtain first-order and second-order characterizations, both necessary and sufficient, for directional metric subregula...

Let X and Y be Hilbert C∗-modules over a C∗-algebra, and φ : X ×Y → [0,∞) be a function. A (not necessarily linear) mapping f : X → Y is called a φ-perturbed adjointable mapping if there exists a (not necessarily linear) mapping g : Y → X such that ‖〈f(x), y〉 − 〈x, g(y)〉‖ ≤ φ(x, y) (x ∈ X , y ∈ Y). In this paper, we investigate the generalized Hyers–Ulam–Rassias stability of adjointable mapping...

This paper discusses automatic acquisition of predicate-argument mapping information from multilingual texts. The lexicon of our NLP system abstracts the language-dependent portion of predicate-argument mapping information from the core meaning of verb senses (i.e. semantic concepts as defined in the knowledge base). We represent this mapping information in terms of cross-linguistically general...

The canonical redshift−scale factor relation, 1/a = 1 + z, is a key element in the standard ΛCDM model of the big bang cosmology. Despite its fundamental role, this relation has not yet undergone any observational tests since Lemaı̂tre and Hubble established the expansion of the Universe. It is strictly based on the assumption of the Friedmann–Lemaı̂tre–Robertson–Walker metric describing a locall...

In this paper we show that metric regularity and strong metric regularity of a set-valued mapping imply convergence of inexact iterative methods for solving a generalized equation associated with this mapping. To accomplish this, we first focus on the question how these properties are preserved under changes of the mapping and the reference point. As an application, we consider discrete approxi...