Jensen-二次函数方程及其Hyers—Ulam稳定性

纪培胜, 赵英姿

数学学报 ›› 2015, Vol. 58 ›› Issue (2) : 251-260.

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数学学报 ›› 2015, Vol. 58 ›› Issue (2) : 251-260. DOI: 10.12386/A2015sxxb0025
论文

Jensen-二次函数方程及其Hyers—Ulam稳定性

    纪培胜, 赵英姿
作者信息 +

On a Jensen-quadratic Functional Equation and Its Hyers-Ulam Stability

    Pei Sheng JI, Ying Zi ZHAO
Author information +
文章历史 +

摘要

给出Jensen-二次函数方程f((x1+x2)/2,y1+y2)+f((x1+x2)/2,y1-y2)=f(x1,y1)+f(x1,y2)+f(x2,y1)+f(x2,y2)的一般解, 并研究了它的Hyers—Ulam稳定性.

Abstract

We obtain the general solution and stability of the Jensen-quadratic functional equation f((x1+x2)/2,y1+y2)+f((x1+x2)/2,y1-y2)=f(x1,y1)+f(x1,y2)+f(x2,y1)+f(x2,y2).

关键词

Hyers&mdash / Ulam稳定性 / 混合三次-二次函数方程 / Jensen-二次函数方程

Key words

Hyers-Ulam stability / mixed cubic-quadratic function / Jensen-quadratic functional equation

引用本文

导出引用
纪培胜, 赵英姿. Jensen-二次函数方程及其Hyers—Ulam稳定性. 数学学报, 2015, 58(2): 251-260 https://doi.org/10.12386/A2015sxxb0025
Pei Sheng JI, Ying Zi ZHAO. On a Jensen-quadratic Functional Equation and Its Hyers-Ulam Stability. Acta Mathematica Sinica, Chinese Series, 2015, 58(2): 251-260 https://doi.org/10.12386/A2015sxxb0025

参考文献

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[3] Brillouět-Bellout N., Brzdek J., Ciepliński K., On some recent developments in Ulam's type stability, Abstr. Appl. Anal., 2012, Art. ID 716936, 41 pages.

[4] Chang I. S., Jung Y. S., Stability of a functional equation deriving from cubic and quadratic functions, J. Math. Anal. Appl., 2003, 283: 491-500.

[5] Ji P., Liu W., On a Cauchy-quadratic functional equation and its Hyers-Ulam-Rassias stability, J. Shandong Univerity (Natural Science), to appear (in Chinese); Hyers-Ulam-Rassias stability, to appear.

[6] Jun K. W., Kim H. M., The generalized Hyers-Ulam-Rassias stability of cubic functional equation, J. Math. Anal. Appl., 2002, 274: 867-878.

[7] Jung S. M., Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, Springer Optimization and Its Applications, 48, Springer, New York, 2011.

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基金

国家自然科学基金(10971117)

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