Stability of the generalized alternative cauchy equation期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Stability of the generalized alternative cauchy equation

Authors:

Institution:

(1) Institute of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Cracow, Poland;(2) Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Cracow, Poland

Abstract:

Let G be a commutative semigroup and letL be a complete Archimedean Riesz Space. Suppose thatF: G → L satisfies for somee ∈ L ₊ the inequality

$\left| {|F(x + y)| - |F(x) + F(y)|} \right| \leqslant e for x, y \in G.$

Then there exists a unique additive mappingA : G → L such that

$\left| {F(x) - A(x)} \right| \leqslant e for x \in G.$

As the method of the proof we use the Johnson-Kist Representation Theorem.

Keywords:

and phrases" target="_blank"> and phrases An alternative Cauchy equation the Johnson-Kist Representation Theorem

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