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Open AccessArticle

Generalized Hyers–Ulam Stability of the Additive Functional Equation

by 1 and 2,*
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)
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
MDPI and ACS Style

Lee, Y.-H.; Kim, G.H. Generalized Hyers–Ulam Stability of the Additive Functional Equation. Axioms 2019, 8, 76.

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Axioms, EISSN 2075-1680, Published by MDPI AG
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