Kannappan和Van vleck泛函方程的超稳定性

The Journal of Nonlinear Sciences and Applications Pub Date : 2018-05-17 DOI:10.22436/JNSA.011.07.03

Belfakih Keltouma, E. Elhoucien, T. Rassias, R. Ahmed

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引用次数: 8

摘要

本文证明了泛函方程μ(y)f(xσ(y)z0)±f(xyz0) = 2f(x)f(y)， x,y∈S， μ(y)f(σ(y)xz0)±f(xyz0) = 2f(x)f(y)， x,y∈S的超稳定性定理，其中S是半群，σ是S的对合态射，μ: S−→C是一个有界乘法函数，使得μ(xσ(x))对所有x∈S都= 1,z0在S的中心。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Superstability of Kannappan's and Van vleck's functional equations

In this paper, we prove the superstability theorems of the functional equations μ(y)f(xσ(y)z0)± f(xyz0) = 2f(x)f(y), x,y ∈ S, μ(y)f(σ(y)xz0)± f(xyz0) = 2f(x)f(y), x,y ∈ S, where S is a semigroup, σ is an involutive morphism of S, and μ : S −→ C is a bounded multiplicative function such that μ(xσ(x)) = 1 for all x ∈ S, and z0 is in the center of S.

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The Journal of Nonlinear Sciences and Applications

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