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Generalized Hyers–Ulam Stability of the Additive Functional Equation

1
Department of Mathematics Education, Gongju National University of Education, Gongju 32553, Korea
2
Department of Mathematics, Kangnam University, Yongin 16979, Korea
*
Author to whom correspondence should be addressed.
Axioms 2019, 8(2), 76; https://doi.org/10.3390/axioms8020076
Received: 2 May 2019 / Revised: 20 June 2019 / Accepted: 21 June 2019 / Published: 25 June 2019
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
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PDF [258 KB, uploaded 25 June 2019]

Abstract

We will prove the generalized Hyers–Ulam stability and the hyperstability of the additive functional equation f(x1 + y1, x2 + y2, …, xn + yn) = f(x1, x2, … xn) + f(y1, y2, …, yn). By restricting the domain of a mapping f that satisfies the inequality condition used in the assumption part of the stability theorem, we partially generalize the results of the stability theorems of the additive function equations. View Full-Text
Keywords: additive (Cauchy) equation; additive mapping; Hyers–Ulam stability; generalized Hyers–Ulam stability; hyperstability additive (Cauchy) equation; additive mapping; Hyers–Ulam stability; generalized Hyers–Ulam stability; hyperstability
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Lee, Y.-H.; Kim, G.H. Generalized Hyers–Ulam Stability of the Additive Functional Equation. Axioms 2019, 8, 76.

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