In vector optimization one assumes in general that a partial ordering is given by some
nontrivial convex cone K in the considered space Y. But already in 1974 in one of the first …

Cone-valued maps are special set-valued maps where the image sets are cones. Such
maps play an important role in optimization, for instance in optimality conditions or in the …

In this paper, we investigate the general solution of a new quadratic functional equation of
the form∑ 1≤ i< j< k≤ r ϕ li+ lj+ lk= r− 2∑ i= 1, i≠ jr ϕ li+ lj+− r 2+ 32 r−/2∑ i= 1 r ϕ li. We …

By using several auxiliary results on relations and their intersection convolutions, we give
some necessary and sufficient conditions in order that a certain additive partial selection …

We introduce some fuzzy set-valued functional equations, ie the generalized Cauchy type
(in n variables), the Quadratic type, the Quadratic-Jensen type, the Cubic type and the Cubic …

A classical result by Crouzeix (1977) states that a real-valued function is convex if and only if
any function obtained from it by adding a linear functional is quasiconvex. The principal aim …

In this paper, we investigate the general solution of a new quadratic functional equation. We
prove that a function admits, in appropriate conditions, a unique quadratic mapping …

The purpose of this paper was to characterize the set-valued dynamics related to
generalized Euler–Lagrange set-valued functional equations. More importantly, the …

In this chapter we recall basic concepts of partially ordered spaces and basic results on
ordering cones and dual cones. We introduce variable ordering structures and examine their …

In the first part of this paper, we provide several historical facts on the famous Hyers–Ulam
stability theorems, Hahn–Banach extension theorems, and their set-valued generalizations …