Solution and stability of an $n$-variable additive functional equation

Solution and stability of an $n$-variable additive functional equation

In this paper, we investigate the general solution and the Hyers-Ulam stability of $n$-variable additive functional equation of the form $$\Im\left(\sum_{i=1}^{n}(-1)^{i+1}x_i\right)=\sum_{i=1}^{n}(-1)^{i+1}\Im (x_i),$$ where $n$ is a positive integer with $n \ge 2$, in Banach spaces by using the di...

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Veröffentlicht in:한국수학논문집, 28(3) 2020, 28(3), , pp.613-621
Hauptverfasser: Vediyappan Govindan, 이정례, Sandra Pinelas, Abdul Rahim Noorsaba(Department of Mathematics, Government Arts College, Ganapathy Balasubramanian(Department of Mathematics, Government Arts College
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Sprache:eng
Schlagworte:
수학
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Zusammenfassung:In this paper, we investigate the general solution and the Hyers-Ulam stability of $n$-variable additive functional equation of the form $$\Im\left(\sum_{i=1}^{n}(-1)^{i+1}x_i\right)=\sum_{i=1}^{n}(-1)^{i+1}\Im (x_i),$$ where $n$ is a positive integer with $n \ge 2$, in Banach spaces by using the direct method. KCI Citation Count: 0
ISSN:1976-8605
2288-1433
DOI:10.11568/kjm.2020.28.3.613