一类源自可加、二次、三次和四次映射的泛函方程的模糊稳定性

王利广, 刘博

数学学报 ›› 2012, Vol. 55 ›› Issue (5) : 841-854.

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数学学报 ›› 2012, Vol. 55 ›› Issue (5) : 841-854. DOI: 10.12386/A2012sxxb0081
论文

一类源自可加、二次、三次和四次映射的泛函方程的模糊稳定性

    王利广, 刘博
作者信息 +

Fuzzy Stability of a Functional Equation Deriving from Additive, Quadratic,Cubic and Quartic Functions

    Li Guang, WANG Bo LIU
Author information +
文章历史 +

摘要

在模糊Banach空间中研究了混合泛函方程f(x+ky)+f(x-ky)=k2f(x+y)+k2f(x-y)+2(1-k2)f(x)+k2(k2-1)/12( (2y)-4 (y))的Hyers-Ulam稳定性, 这里k>1是固定的一个整数, (y)=f(y)+f(-y).

Abstract

We investigate the Hyers-Ulam stability of the following mixed type functional equations f(x+ky)+f(x-ky)=k2f(x+y)+k2f(x-y)+2(1-k2)f(x) +k2(k2-1)/12( (2y)-4 (y))in fuzzy Banach spaces where k>1 is a fixed integer and (y)=f(y)+f(-y).

关键词

稳定性 / 二次泛函方程 / 三次泛函方程 / 四次泛函方程 / 模糊Banach空间

Key words

Hyers-Ulam stability / quadratic functional equation / cubic functional equation / quartic functional equation

引用本文

导出引用
王利广, 刘博. 一类源自可加、二次、三次和四次映射的泛函方程的模糊稳定性. 数学学报, 2012, 55(5): 841-854 https://doi.org/10.12386/A2012sxxb0081
Li Guang, WANG Bo LIU. Fuzzy Stability of a Functional Equation Deriving from Additive, Quadratic,Cubic and Quartic Functions. Acta Mathematica Sinica, Chinese Series, 2012, 55(5): 841-854 https://doi.org/10.12386/A2012sxxb0081

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)及山东省博士后创新项目(201003044)

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