In this paper, we define a generalized additive set-valued functional equation, which is related to the following generalized additive functional equation: f (x 1 + · · · + x l) = (l – 1)f x 1 + · · · + x l–1 l – 1 + f (x l) for a fixed integer l with l > 1, and prove the Hyers-Ulam stability of the generalized additive set-valued functional equation.

In this paper Gallai’s inequality on the number of edges in critical graphs is generalized for reducible additive induced-hereditary properties of graphs in the following way. Let P1,P2, . . . ,Pk (k ≥ 2) be additive induced-hereditary properties, R = P1◦ P2◦ · · · ◦Pk and δ = ∑k i=1 δ(Pi). Suppose that G is an R-critical graph with n vertices and m edges. Then 2m ≥ δn + δ−2 δ2+2δ−2 n + 2δ δ2+2...

In the context of Social Welfare and Choquet integration, we briefly review, on the one hand, the generalized Gini welfare functions and inequality indices for populations of n ≥ 2 individuals, and on the other hand, the Möbius representation framework for Choquet integration, particularly in the case of k-additive symmetric capacities. We recall the binomial decomposition of OWA functions due ...

Let A be an algebra over the real or complex field F. An additive mapping d : A → A is said to be a left derivation resp., derivation if the functional equation d xy xd y yd x resp., d xy xd y d x y holds for all x, y ∈ A. Furthermore, if the functional equation d λx λd x is valid for all λ ∈ F and all x ∈ A, then d is a linear left derivation resp., linear derivation . An additive mapping G : ...

‎Let $mathscr{L}$ be a commutative subspace lattice generated by finite many commuting independent nests on a complex separable Hilbert space $mathbf{H}$ with ${rm dim}hspace{2pt}mathbf{H}geq 3$‎, ‎${rm Alg}mathscr{L}$‎ ‎the CSL algebra associated with $mathscr{L}$ and $mathscr{M}$ be an algebra containing ${rm Alg}mathscr{L}$‎. ‎This article is aimed at describing the form of‎ ‎additive mapppi...

it is well known that a microperiodic function mapping a topological group into reals, which is continuous at some point is constant. we introduce the notion of a microperiodic multifunction, defined on a topological group with values in a metric space, and study regularity conditions implying an analogous result. we deal with vietoris and hausdorff continuity concepts.stability of microperiodi...

In this paper, a new inequality for generalized convex functions which is related to the left side of generalized Hermite-Hadamard type inequality is obtained. Some applications for some generalized special means are also given.