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

Sandra Pinelas|이정례|Vediyappan Govindan|Abdul Rahim Noorsaba|Ganapathy Balasubramanian
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2020.09|한국수학논문집 (Korean Journal of Mathematics)|제28권 제3호|pp. 613-621

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참고문헌

키워드

Hyers-Ulam stability.Additive functional equation
주제분류수학

초록

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.

Abstract

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.

참고문헌 (16)

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