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Characterizations of biselective operations Devillet, Jimmy ; 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 ▲] Detailed reference viewed: 88 (25 UL)Barycentrically associative and preassociative functions Marichal, Jean-Luc ; Teheux, Bruno 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 ▲] Detailed reference viewed: 123 (19 UL)Algebraic methods for the solution of linear functional equations Kiss, Gergely ; ; in Acta Mathematica Hungarica (2015), 146(1), 128141 Detailed reference viewed: 72 (7 UL)Universal distribution of limit points Meyrath, Thierry ; 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 ▲] Detailed reference viewed: 57 (1 UL) |
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