In this paper, a class of generalized general mixed quasi variational inequalities is introduced and studied. We prove the existence of the solution of the auxiliary problem for the generalized general mixed quasi variational inequalities, suggest a predictor-corrector method for solving the generalized general mixed quasi variational inequalities by using the auxiliary principle technique. If ...

Results on integration by parts and integration by substitution for the variational integral of Henstock are well-known. When real-valued functions are considered, such results also hold for the Generalized Riemann Integral defined by Kurzweil since, in this case, the integrals of Kurzweil and Henstock coincide. However, in a Banach-space valued context, the Kurzweil integral properly contains ...

We give a new time-dependent definition of spline curves in Rn, which extends a recent definition of vector-valued splines introduced by Rodrigues and Silva Leite for the time-independent case. Previous results are based on a variational approach, with lengthy arguments, which do not cover the non-autonomous situation. We show that the previous results are a consequence of the Pontryagin maximu...

In this paper we extend to the vector case the notion of increasing along rays function. The proposed definition is given by means of a nonlinear scalarization through the so-called oriented distance function from a point to a set. We prove that the considered class of functions enjoys properties similar to those holding in the scalar case, with regard to optimization problems, relations with (...

We prove isoperimetric inequalities for general parametric variational double integrals F , whose Lagrangians F depend on the position vector X and on the surface normal N. As an essential tool we introduce Sauvigny’s F -conformal parameters adapted to the parametric integrand and use the notion of generalized mean and Gaussian curvature adapted to the integrand. The special cases of minimal su...

where C ⊆ Rm is a closed convex and pointed cone with nonempty interior intC. (WVVI) was firstly introduced by Giannessi []. It has been shown to have many applications in vector optimization problems and traffic equilibrium problems (e.g., [, ]). Error bounds are to depict the distance from a feasible solution to the solution set, and have played an important role not only in sensitivity an...