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Solution and stability of an $n$-variable additive functional equation
Vediyappan Govindan,이정례,Sandra Pinelas,Abdul Rahim Noorsaba,Ganapathy Balasubramanian 강원경기수학회 2020 한국수학논문집 Vol.28 No.3
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.