Superstability of the equation of quadratic functionals in L p-spaces

被引：0

作者：

Czerwik S. ^{[1
]}

Dłutek K. ^{[1
]}

机构：

[1] Institute of Mathematics, Silesian University of Technology, PL-44-100 Gliwice

来源：

aequationes mathematicae | 2002年 / 63卷 / 3期

关键词：

L[!sup]p[!/sup]-spaces; Quadratic functional equation; Stability;

D O I：

10.1007/s00010-002-8019-3

中图分类号：

学科分类号：

摘要：

Let (X, μ) be an abelian complete measurable group with μ(X) = +∞, and let E be a metric abelian group. Let f : X → E be a function. We will show that if Qf ∈ Lp+ (X × X, E), where Qf(x, y) = 2f(x) + 2f(y) - f(x + y) - f(x - y), x, y ∈ X, then there exists a quadratic function g : X → E, i.e. a function with 2g(x) + 2g(y) = g(x + y) + g(x - y), x, y ∈ X such that f is equal to g almost everywhere with respect to the measure μ. Lp+ denotes the space of functions for witch the upper integral of ∥f∥p is finite. © Birkhäuser Verlag, Basel, 2002.

引用

页码：210 / 219

页数：9

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