We construct a matrix-valued spin-dependent distribution function (MVSD) for massive spin-1/2 fermions and study its properties under Lorentz transformations. Such transformations result in Wigner rotation spin space nontrivial shift space-time, which corresponds to the side jump massless case. express vector axial-vector components of terms MVSD show that they transform Lorentz-covariant manne...

Abstract In this paper, we deal with the sensitivity analysis in vector equilibrium problems by using S -derivative of a set-valued mapping. We first investigate on kind gap function for problems. Based these results, estimations perturbed mapping parametric problem are given. Moreover, provide some examples to illustrate obtained results. Finally, derive solutions via variational system.

‎In this paper‎, ‎we study the Hölder continuity of solution mapping to a parametric variational inequality‎. ‎At first‎, ‎recalling a real-valued gap function of the problem‎, ‎we discuss the Lipschitz continuity of the gap function‎. ‎Then under the strong monotonicity‎, ‎we establish the Hölder continuity of the single-valued solution mapping for the problem‎. ‎Finally‎, ‎we apply these resu...

In this paper we establish two alternative principles of the following type: If X and Y are convex subsets of two locally convex Hausdorff topological vector spaces and F, S : X Y are two set-valued mappings satisfying certain conditions, then either there exists x0 ∈ X such that F(x0) = ∅ or⋂x∈X S(x) = ∅. As first applications of the alternative principles we obtain two matching theorems of Ky...

‎In the paper‎, ‎we study duality for vector equilibrium problems using a concept of generalized convexity in dealing with the quasi-relative interior‎. ‎Then‎, ‎their applications to optimality conditions for quasi-relative efficient solutions are obtained‎. ‎Our results are extensions of several existing ones in the literature when the ordering cones in both the objective space and the constr...

Abstract The aim of this paper is to establish new results on the error bounds for a class vector equilibrium problems with partial order provided by polyhedral cone generated some matrix. We first propose regularized gap functions problem using concept $$\mathcal {G}_{A}$$ G A </m...

We consider the two matrix model with an even quartic potential W (y) = y/4+αy/2 and an even polynomial potential V (x). The main result of the paper is the formulation of a vector equilibrium problem for the limiting mean density for the eigenvalues of one of the matrices M1. The vector equilibrium problem is defined for three measures, with external fields on the first and third measures and ...