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See detailCharacterizations of biselective operations
Devillet, Jimmy UL; Kiss, Gergely

in Acta Mathematica Hungarica (2019), 157(2), 387-407

Let X be a nonempty set and let i,j in {1,2,3,4}. We say that a binary operation F:X^2 -> X is (i,j)-selective if F(F(x_1,x_2),F(x_3,x_4)) = F(x_i,x_j), for all x_1,x_2,x_3,x_4 in X. In this paper we ... [more ▼]

Let X be a nonempty set and let i,j in {1,2,3,4}. We say that a binary operation F:X^2 -> X is (i,j)-selective if F(F(x_1,x_2),F(x_3,x_4)) = F(x_i,x_j), for all x_1,x_2,x_3,x_4 in X. In this paper we provide characterizations of the class of (i,j)-selective operations. We also investigate some subclasses by adding algebraic properties such as associativity or bisymmetry. [less ▲]

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See detailBarycentrically associative and preassociative functions
Marichal, Jean-Luc UL; Teheux, Bruno UL

in Acta Mathematica Hungarica (2015), 145(2), 468-488

We investigate the barycentric associativity property for functions with indefinite arities and discuss the more general property of barycentric preassociativity, a generalization of barycentric ... [more ▼]

We investigate the barycentric associativity property for functions with indefinite arities and discuss the more general property of barycentric preassociativity, a generalization of barycentric associativity which does not involve any composition of functions. We also provide a generalization of Kolmogoroff-Nagumo's characterization of the quasi-arithmetic mean functions to barycentrically preassociative functions. [less ▲]

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See detailAlgebraic methods for the solution of linear functional equations
Kiss, Gergely UL; Varga, Adrienn; Vincze, Csaba

in Acta Mathematica Hungarica (2015), 146(1), 128141

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See detailUniversal distribution of limit points
Meyrath, Thierry UL; Niess, Markus

in Acta Mathematica Hungarica (2011), 133(3), 288-303

We consider sequences of functions that have in some sense a universal distribution of limit points of zeros in the complex plane. In particular, we prove that functions having universal approximation ... [more ▼]

We consider sequences of functions that have in some sense a universal distribution of limit points of zeros in the complex plane. In particular, we prove that functions having universal approximation properties on compact sets with connected complement automatically have such a universal distribution of limit points. Moreover, in the case of sequences of derivatives, we show connections between this kind of universality and some rather old results of Edrei/MacLane and Pólya. Finally, we show the lineability of the set of what we call Jentzsch-universal power series. [less ▲]

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