一类可加和二次混合泛函方程的稳定性

王利广, 李静

数学学报 ›› 2013, Vol. 56 ›› Issue (4) : 583-596.

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数学学报 ›› 2013, Vol. 56 ›› Issue (4) : 583-596. DOI: 10.12386/A2013sxxb0059
论文

一类可加和二次混合泛函方程的稳定性

    王利广1, 李静2
作者信息 +

On the Stability of a Mixed Functional Equations Deriving from Additive Mappings and Quadratic Mappings

    Li Guang WANG1, Jing LI2
Author information +
文章历史 +

摘要

本文研究了一类新的源自可加映射和二次映射的混合泛函方程
f(x + 2y) + f(x − 2y) = f(x + y) + f(x − y) + 3f(2y) − 6f(y)
及其在拟β赋范线性空间中的Hyers-Ulam稳定性.

Abstract

We introduce a new class of functional equations
f(x + 2y) + f(x − 2y) = f(x + y) + f(x − y) + 3f(2y) − 6f(y)
deriving from additive mappings and quadratic mappings and consider its Hyers-Ulam stability on quasi-β-normed linear spaces.

关键词

可加映射 / 二次映射 / 拟β赋范线性空间

Key words

additive mapping / quadratic mapping / quasi-β-normed linear space

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王利广, 李静. 一类可加和二次混合泛函方程的稳定性. 数学学报, 2013, 56(4): 583-596 https://doi.org/10.12386/A2013sxxb0059
Li Guang WANG, Jing LI. On the Stability of a Mixed Functional Equations Deriving from Additive Mappings and Quadratic Mappings. Acta Mathematica Sinica, Chinese Series, 2013, 56(4): 583-596 https://doi.org/10.12386/A2013sxxb0059

参考文献

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基金

国家自然科学基金资助项目(10971117);山东省自然科学基金(ZR2012AM024)

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