In this paper, we introduce the concept of approximate solutions for set-valued mappings and provide a sufficient condition for the existence of approximate solutions of set-valued mappings. We obtain an approximate variational principle for set-valued mappings. Copyright Springer-Verlag Berlin...

In this paper, three equivalents of a corollary of the general approximate variational principle for set-valued maps which we obtained in [5] are derived. Applying a corollary of the general approximate variational principle, we obtain existence theorems for efficient solutions to vector...

In this paper, three equivalents of a corollary of the general approximate variational principle for set-valued maps which we obtained in [5] are derived. Applying a corollary of the general approximate variational principle, we obtain existence theorems for efficient solutions to vector...

In this paper, we introduce the symmetric strong vector quasi-equilibrium problem. We then demonstrate that the symmetric strong vector quasi-equilibrium problem is solvable under the suitable assumptions. As an application, we get an existence theorem of the strong saddle points of...

This paper is devoted to the Levitin–Polyak well-posedness by perturbations for a class of general systems of set-valued vector quasi-equilibrium problems (SSVQEP) in Hausdorff topological vector spaces. Existence of solution for the system of set-valued vector quasi-equilibrium problem with...

The connection between fluid dynamics and classical statistical mechanics has motivated in the past mathematical investigations of the incompressible Navier–Stokes (NS) equations (INSE) by means of an asymptotic kinetic theory. This feature has suggested the search for possible alternative...

This paper is devoted to the Levitin–Polyak well-posedness by perturbations for a class of general systems of set-valued vector quasi-equilibrium problems (SSVQEP) in Hausdorff topological vector spaces. Existence of solution for the system of set-valued vector quasi-equilibrium problem with...

In the present study we have formulated a generalization of entropy optimization problems (GEOP), proposed sufficient conditions for the existence of solution. We have suggested also a new method based on a priori evaluations and Newton's methods for calculation of Langrange multipliers....

In this paper, we deal with the Lp(p1) solutions to one dimensional backward stochastic differential equations (BSDEs) with discontinuous generators. We obtain an existence theorem of Lp solutions for BSDEs whose generators satisfy a kind of discontinuous condition in y and are uniformly...