Włodzimierz Fechner

The modularity law in some classes of aggregation operators

Abstract In this study, we consider the functional equation of modularity in a special class of aggregation operators with an absorbing element. First, we focus on the modularity between commutative binary operators and their duals, and then we examine the modularity for operators from the class of 2-uninorms, which generalize nullnorms by extending their certain conditions. In particular, for these operators, depending on the positions of their neutral elements and possessing the same absorbing element, we obtain positive and negative results, which are analogous to the results in the general case for operators with different absorbing elements.

On functions with the Cauchy difference bounded by a functional. Part II

We are going to consider the functional inequality f ( x + y ) − f ( x ) − f ( y ) ≥ ϕ ( x , y ) , x , y ∈ X , where ( X , + ) is an abelian group, and ϕ : X × X → ℝ and f : X → ℝ are unknown mappings. In particular, we will give conditions which force biadditivity and symmetry of ϕ and the representation f ( x ) = ( 1 / 2 ) ϕ ( x , x ) + a ( x ) for x ∈ X , where a is an additive function. In the present paper, we continue and develop our earlier studies published by the author (2004).

Inequalities Characterizing Linear-Multiplicative Functionals

We prove, in an elementary way, that if a nonconstant real-valued mapping defined on a real algebra with a unit satisfies certain inequalities, then it is a linear and multiplicative functional. Moreover, we determine all Jensen concave and supermultiplicative operators , where and are compact Hausdorff spaces.

On a question of J.M. Rassias

Answering a problem posed by John Michael Rassias we study the following functional inequality:

Sandwich Theorems for Orthogonally Additive Functions

f(x + y + xy) \leq f(x) + f(y) + f(xy)

A note on a result of I. Gusić on two inequalities in lattice-ordered groups

with real unknown mapping \(f\). DOI: 10.1017/S0004972713000889

Comparisons of Means and Related Functional Inequalities

The purpose of the chapter is to deal with some old and a few new functional inequalities which are motivated by well-known estimates on the real line or on an interval which involve the exponential function. We are concerned with the following six functional inequalities: Open image in new window and