A concept of weak $f$-property for a set-valued mapping is introduced‎, ‎and then under some suitable assumptions‎, ‎which do not involve any information‎ ‎about the solution set‎, ‎the lower semicontinuity of the solution mapping to‎ ‎the parametric‎ ‎set-valued vector equilibrium-like problems are derived by using a density result and scalarization method‎, ‎where the‎ ‎constraint set $K$...

The main purpose of this paper is to obtain sufficient conditions for existence of points of coincidence and common fixed points for a pair of self mappings satisfying some expansive type conditions in $b$-metric spaces. Finally, we investigate that the equivalence of one of these results in the context of cone $b$-metric spaces cannot be obtained by the techniques using scalarization function....

Benefitting from the unequaled precision of pulsar timing technique, binary pulsars are important testbeds gravity theories, providing some tightest bounds on alternative theories gravity. One class well-motivated scalar-tensor gravity, predict large deviations general relativity for neutron stars through a nonperturbative phenomenon known as spontaneous scalarization. This effect, which cannot...

We present a new family of exact black hole configurations, which is solution to generalized Einstein-Maxwell-Dilaton setup in arbitrary dimension. These solutions are asymptotically Lifshitz for any dynamical critical exponent $z\ensuremath{\ge}1$. It turns out that the existence nontrivial scalar field direct consequence breaking spacetime isotropic scaling symmetry. This accepts various inte...

A new parameterized binary relation is used to define minimality concepts in vector optimization. To simplify the problem of determining minimal elements the method of scalarization is applied. Necessary and sufficient conditions for the existence of minimal elements with respect to the scalarized problems are given. The multiplier rule of Lagrange is generalized. As a necessary minimality cond...

It is known that vector variational inequality models arises from vector optimization and vector traac equilibria. In this paper, existence results of a solution for a generalized pre-vector variational inequality and a generalized pre-quasi-vector variational inequality are established. The main condition used is that the underlying vector-valued function is assumed to be cone-quasi-convex. Th...

Our goal in this talk is to present unifying concepts for both stochastic and robust optimization problems involving infinite uncertainty sets. We apply methods from vector optimization in general spaces, set-valued optimization and scalarization techniques to develop a unified characterization of different concepts of robust optimization and stochastic programming. These methods provide new in...

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 (...

The concepts of well-posedness of l-set optimization problem under variable order structure are introduced, the metric characterizations and sufficient criteria of well-posedness of a l-set optimization problem are proposed, and the equivalent relations between the well-posedness of l-set optimization problem and that of a scalarization minimization problem are established. Finally, by discussi...