Characterization of field homomorphisms through Pexiderized functional equations

in Journal of Difference Equations and Applications (in press)

On biselective operations

Scientific Conference (2018, June 07)

See attached file

The discrete Pompeiu problem on the plane

in Monatshefte für Mathematik (2018)

We say that a finite subset $E$ of the Euclidean plane $\R^2$ has the discrete Pompeiu property with respect to isometries (similarities), if, whenever $f:\R^2\to \C$ is such that the sum of the values of ... [more ▼]

We say that a finite subset $E$ of the Euclidean plane $\R^2$ has the discrete Pompeiu property with respect to isometries (similarities), if, whenever $f:\R^2\to \C$ is such that the sum of the values of $f$ on any congruent (similar) copy of $E$ is zero, then $f$ is identically zero. We show that every parallelogram and every quadrangle with rational coordinates has the discrete Pompeiu property with respect to isometries. We also present a family of quadrangles depending on a continuous parameter having the same property. We investigate the weighted version of the discrete Pompeiu property as well, and show that every finite linear set with commensurable distances has the weighted discrete Pompeiu property with respect to isometries, and every finite set has the weighted discrete Pompeiu property with respect to similarities. [less ▲]

Derivations and differential operators on rings and fields

Scientific Conference (2018, June)

On functional equations characterizing derivations: methods and examples

in Results in Mathematics (2018)

Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions ... [more ▼]

Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and automorphisms are additive functions satisfying some further functional equations as well. It is an important question that how these morphisms can be characterized among additive mappings in general. The paper contains some multivariate characterizations of higher order derivations. The univariate characterizations are given as consequences by the diagonalization of the multivariate formulas. This method allows us to refine the process of computing the solutions of univariate functional equations of the form ∑k=1nxpkfk(xqk)=0, where pk and qk (k=1,…,n) are given nonnegative integers and the unknown functions f1,…,fn:R→R are supposed to be additive on the ring R. It is illustrated by some explicit examples too. As another application of the multivariate setting we use spectral analysis and spectral synthesis in the space of the additive solutions to prove that it is spanned by differential operators. The results are uniformly based on the investigation of the multivariate version of the functional equations. [less ▲]

Pointwise regularity of parameterized affine zipper fractal curves fractal curves

in Nonlinearity (2018), 31(5),

We study the pointwise regularity of zipper fractal curves generated by affine mappings. Under the assumption of dominated splitting of index-1, we calculate the Hausdorff dimension of the level sets of ... [more ▼]

We study the pointwise regularity of zipper fractal curves generated by affine mappings. Under the assumption of dominated splitting of index-1, we calculate the Hausdorff dimension of the level sets of the pointwise Hölder exponent for a subinterval of the spectrum. We give an equivalent characterization for the existence of regular pointwise Hölder exponent for Lebesgue almost every point. In this case, we extend the multifractal analysis to the full spectrum. In particular, we apply our results for de Rham’s curve. [less ▲]

Associative idempotent nondecreasing functions are reducible

in Semigroup Forum (2017)

An n-variable associative function is called reducible if it can be written as a composition of a binary associative function. In this paper we summarize the known results when the function is defined on ... [more ▼]

An n-variable associative function is called reducible if it can be written as a composition of a binary associative function. In this paper we summarize the known results when the function is defined on a chain and nondecreasing. The main result of this paper shows that associative idempotent and nondecreasing functions are uniquely reducible. [less ▲]

Generalization of Czoga\l a-Drewniak Theorem for $n$-ary semigroups

in Torra, Vicenç; Mesiar, Radko; De Baets, Bernard (Eds.) Aggregation Functions in Theory and in Practice (2017)

We investigate n-ary semigroups as a natural generalization of binary semigroups. We refer it as a pair (X,F_n), where X is a set and an n-associative function F_n : X^n -> X is defined on X. We show that ... [more ▼]

We investigate n-ary semigroups as a natural generalization of binary semigroups. We refer it as a pair (X,F_n), where X is a set and an n-associative function F_n : X^n -> X is defined on X. We show that if F_n is idempotent, n-associative function which is monotone in each of its variables, defined on an interval I and has a neutral element, then F_n is combination of the minimum and maximum operation. Moreover we can characterize the n-ary semigroups (I,F_n) where F_n has the previous properties. [less ▲]

On spectral analysis in varieties containing the solutions of inhomogeneous linear functional equations

in Aequationes Mathematicae (2017)

The aim of the paper is to investigate the solutions of special inhomogeneous linear functional equations using spectral analysis in a translation invariant closed linear subspace of additive ... [more ▼]

The aim of the paper is to investigate the solutions of special inhomogeneous linear functional equations using spectral analysis in a translation invariant closed linear subspace of additive/multiadditive functions containing the restrictions of the solutions to finitely generated fields. The application of spectral analysis in some related varieties is a new and important trend in the theory of functional equations; especially they have successful applications in the case of homogeneous linear functional equations. The foundations of the theory can be found in Kiss and Varga (Aequat Math 88(1):151–162, 2014) and Kiss and Laczkovich (Aequat Math 89(2):301–328, 2015). We are going to adopt the main theoretical tools to solve some inhomogeneous problems due to Koclȩga-Kulpa and Szostok (Ann Math Sylesianae 22:27–40, 2008), see also Koclȩga-Kulpa and Szostok (Georgian Math J 16:725–736, 2009; Acta Math Hung 130(4):340–348, 2011). They are motivated by quadrature rules of approximate integration. [less ▲]

International Symposium on Aggregation and Structures (ISAS 2016) - Book of abstracts

Book published by NA (2016)