共查询到20条相似文献,搜索用时 15 毫秒
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Mahmud Bajraktarević 《Aequationes Mathematicae》1985,29(1):175-182
Sans résumé
Dedié à János Aczél à l'occasion de son 60ème anniversaire 相似文献
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Claudi Alsina 《Aequationes Mathematicae》1991,41(1):94-102
Summary We give a characterization of the weighted arithmetic mean onR
n by solving a functional equation motivated by a problem of synthesizing multidimensional judgements consistent with nonsingular linear transformations.Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth. 相似文献
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Summary AssumeE is a real topological vector space,F is a real Banach space,K is a discrete subgroup ofF andC is a symmetric, convex and compact subset ofF such thatK (6C) = {0}. If a functionh:E F is continuous at at least one point andh(x + y) – h(x) – h(y) K + C for allx, y E, then there exists a continuous linear functiona:E F such thath(x) – a(x) K + C for everyx E. 相似文献
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B. Fuglede 《Aequationes Mathematicae》1990,39(2-3):198-203
Summary It is shown that a finely superharmonic function in a planar fine domainU is greater than or equal to its lower integral with respect to harmonic measure associated with any bounded finely open setV with fine closure contained inU. Examples are given showing that this result does not extend to dimension 3 or more (unlessf is supposed to be, e.g., lower bounded onV) and also that the integral need not exist. 相似文献
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Summary In this paper we give a new definition of a probabilistic normed space. This definition, which is based on a characterization of normed spaces by means of a betweenness relation, includes the earlier definition of A. N. erstnev as a special case and leads naturally to the definition of the principal class of probabilistic normed spaces, the Menger spaces. 相似文献
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Thomas Riedel 《Aequationes Mathematicae》1991,41(1):192-211
Summary Recently R. C. Powers characterized the order automorphisms of the space of nondecreasing functions from one compact real interval to another [6, 7]. In this paper we show how his results, as well as the lattice-theoretic techniques which he employed, can be used to obtain solutions of Cauchy's equation for certain classes of semigroups (triangle functions) on the space + of probability distribution functions of nonnegative random variables. 相似文献
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A contribution to a theorem of Ulam and Mazur 总被引:3,自引:0,他引:3
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Janusz Brzdęk 《Aequationes Mathematicae》1993,46(1-2):56-75
Summary While looking for solutions of some functional equations and systems of functional equations introduced by S. Midura and their generalizations, we came across the problem of solving the equationg(ax + by) = Ag(x) + Bg(y) + L(x, y) (1) in the class of functions mapping a non-empty subsetP of a linear spaceX over a commutative fieldK, satisfying the conditionaP + bP P, into a linear spaceY over a commutative fieldF, whereL: X × X Y is biadditive,a, b K\{0}, andA, B F\{0}.
Theorem.Suppose that K is either R or C, F is of characteristic zero, there exist A
1,A
2,B
1,B
2, F\ {0}with L(ax, y) = A
1
L(x, y), L(x, ay) = A
2
L(x, y), L(bx, y) = B
1
L(x, y), and L(x, by) = B
2
L(x, y) for x, y X, and P has a non-empty convex and algebraically open subset. Then the functional equation (1)has a solution in the class of functions g: P Y iff the following two conditions hold: L(x, y) = L(y, x) for x, y X, (2)if L 0, then A
1 =A
2,B
1 =B
2,A = A
1
2
,and B = B
1
2
. (3)
Furthermore, if conditions (2)and (3)are valid, then a function g: P Y satisfies the equation (1)iff there exist a y
0
Y and an additive function h: X Y such that if A + B 1, then y
0 = 0;h(ax) = Ah(x), h(bx) =Bh(x) for x X; g(x) = h(x) + y
0 + 1/2A
1
-1
B
1
-1
L(x, x)for x P. 相似文献
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Zenon Moszner 《Aequationes Mathematicae》1987,32(1):297-303
Sans résumé
Dédié à Monsieur le Professeur Otto Haupt à l'occasion de son centenaire avec les meilleurs vœux. 相似文献