Korean J. Math.  Vol 28, No 3 (2020)  pp.613-621
DOI: https://doi.org/10.11568/kjm.2020.28.3.613

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

Vediyappan Govindan, Jung-Rye Lee, Sandra Pinelas, Abdul Rahim Noorsaba, Ganapathy Balasubramanian


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.


Additive functional equation; Hyers-Ulam stability.

Subject classification

39B52, 32B72, 32B82, 46H25.


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