| 2-Banach空间上三次-四次混合型函数方程的Hyers-Ulam-Rassias稳定性 |
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| 引用本文： | 王春,许天周. 2-Banach空间上三次-四次混合型函数方程的Hyers-Ulam-Rassias稳定性[J]. 数学物理学报(A辑), 2020, 0(2): 352-368 |
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| 作者姓名： | 王春 许天周 |
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| 作者单位： | 长治学院数学系;北京理工大学数学与统计学院 |
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| 基金项目： | 山西省自然科学基金(201801D121024);山西省高等学校科技创新项目(2019L0903)。 |
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| 摘 要： | 该文研究了2-Banach空间上三次-四次混合型函数方程f(kx+y)+f(kx-y)=(k^2+k)/2[f(x+y)+f(x-y)]+(k^2-k)/2[f(-x-y)+f(y-x)]+(k^4+k^3-k^2-k)f(x)+(k^4-k^3-k^2+k)f(-x)-(k^2-1)f(y)-(k^2-1)f(-y)的一般解和Hyers-Ulam-Rassias稳定性,这里k>1.该文的结果提升和推广了已有的相关结果.
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| 关 键 词： | HYERS-ULAM-RASSIAS稳定性 一般解 三次映射 四次映射 2-Banach空间 |
Hyers-Ulam-Rassias Stability of a Mixed Type Cubic-Quartic Functional Equation in 2-Banach Spaces |
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| Wang Chun,Xu Tianzhou. Hyers-Ulam-Rassias Stability of a Mixed Type Cubic-Quartic Functional Equation in 2-Banach Spaces[J]. Acta Mathematica Scientia, 2020, 0(2): 352-368 |
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| Authors: | Wang Chun Xu Tianzhou |
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| Affiliation: | (Department of Mathematics,Changzhi University,Shanxi Changzhi 046011;School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081) |
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| Abstract: | In this paper,we investigate the general solution and the Hyers-Ulam-Rassias stability of the mixed type cubic-quartic functional equation f(kx+y)+f(kx-y)=(k^2+k)/2[f(x+y)+f(x-y)]+(k^2-k)/2[f(-x-y)+f(y-x)]+(k^4+k^3-k^2-k)f(x)+(k^4-k^3-k^2+k)f(-x)-(k^2-1)f(y)-(k^2-1)f(-y)in 2-Banach spaces,where k>1.The results improve and extend some recent results. |
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| Keywords: | Hyers-Ulam-Rassias stability General solution Cubic function Quartic function 2-Banach space |
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