Cauchy-三次函数方程及其Hyers-Ulam稳定性

纪培胜, 魏然红, 刘荣荣

数学学报 ›› 2014, Vol. 57 ›› Issue (3) : 559-568.

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数学学报 ›› 2014, Vol. 57 ›› Issue (3) : 559-568. DOI: 10.12386/A2014sxxb0052
论文

Cauchy-三次函数方程及其Hyers-Ulam稳定性

    纪培胜, 魏然红, 刘荣荣
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On a Cauchy-Cubic Functional Equation and Its Hyers-Ulam Stability

    Pei Sheng JI, Ran Hong WEI, Rong Rong LIU
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文章历史 +

摘要

给出Cauchy-三次函数方程f（x1+x2,2y1+y2）+{f（x1+x2,2y1-y2）}={2f（x1,y1+y2）}+{2f（x1,y1-y2）}+{12f（x1,y1）}+{2f（x2,y1+y2）}+{2f（x2,y1-y2）}+{12f（x2,y1）}的一般解,并用直接方法和不动点方法研究它在Banach空间上的Hyers-Ulam稳定性及模糊稳定性.

Abstract

We obtain the general solution and the generalized Hyers-Ulam stability of the Cauchy-cubic functional equation f(x1+x2,2y1+y2)+{f(x1+x2,2y1-y2)}={2f(x1,y1+y2)}+{2f(x1,y1-y2)}+{12f(x1,y1)}+{2f(x2,y1+y2)}+{2f(x2,y1-y2)}+{12f(x2,y1)} in Banach space and fuzzy Banach space using the direct method and the fixed point method, respectively.

关键词

Hyers-Ulam稳定性 / Cauchy-三次函数方程 / 四次函数方程

Key words

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

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纪培胜, 魏然红, 刘荣荣. Cauchy-三次函数方程及其Hyers-Ulam稳定性. 数学学报, 2014, 57(3): 559-568 https://doi.org/10.12386/A2014sxxb0052
Pei Sheng JI, Ran Hong WEI, Rong Rong LIU. On a Cauchy-Cubic Functional Equation and Its Hyers-Ulam Stability. Acta Mathematica Sinica, Chinese Series, 2014, 57(3): 559-568 https://doi.org/10.12386/A2014sxxb0052

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基金

国家自然科学基金资助项目（10971117）
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