THE STABILITY OF ADDITIVE (<i>α</i>, <i>β</i>)-FUNCTIONAL EQUATIONS

Ziying Lu; Gang Lu; Yuanfeng Jin; Choonkil Park

doi:10.11948/20190075

2019 Volume 9 Issue 6

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Ziying Lu, Gang Lu, Yuanfeng Jin, Choonkil Park. THE STABILITY OF ADDITIVE (α, β)-FUNCTIONAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2019, 9(6): 2295-2307. doi: 10.11948/20190075

Citation:

Ziying Lu, Gang Lu, Yuanfeng Jin, Choonkil Park. THE STABILITY OF ADDITIVE (α, β)-FUNCTIONAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2019, 9(6): 2295-2307. doi: 10.11948/20190075

THE STABILITY OF ADDITIVE (α, β)-FUNCTIONAL EQUATIONS

1.
Department of Mathematics, School of Science, ShenYang University of Technology, Shenyang 110870, China
2.
Department of Mathematics, Yanbian University, Yanji 133001, China
3.
Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea

Corresponding authors: Email address:lvgang1234@163.com(G. Lu); Email address:yfkim@ybu.edu.cn(Y. Jin)
Fund Project: The authors were supported by (No.11761074), the projection of the Department of Science and Technology of JiLin Province(No.JJKH20170453KJ) and the Education Department of Jilin Province (No. 20170101052JC) and Natural Science Fund of Liaoning Province (No. 201602547)

Abstract

Abstract

In this paper, we investigate the following $(\alpha, \beta)$-functional equations $ \begin{eqnarray}\label{0.1} 2f(x)+2f(z)=f(x-y)+\alpha^{-1}f(\alpha (x+z))+\beta^{-1}f(\beta(y+z)), ~~~(0.1) \\ \label{0.2} 2f(x)+2f(y)=f(x+y)+\alpha^{-1}f(\alpha(x+z)) +\beta^{-1}f(\beta(y-z)), ~~~(0.2) \end{eqnarray} $ where $\alpha, \beta$ are fixed nonzero real numbers with $\alpha^{-1}+\beta^{-1}\neq 3$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the $(\alpha, \beta)$-functional equations $(0.1)$ and $(0.2)$ in non-Archimedean Banach spaces.
- Hyers-Ulam stability /
- additive $(\alpha, \beta)$-functional equation /
- fixed point method /
- direct method /
- non-Archimedean Banach space
MSC: 39B52, 39B62, 47H10

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References

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