Generalized Hyers–Ulam Stability of the Additive Functional Equation

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 stab...

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Bibliographic Details
Published in:Axioms 2019-06, Vol.8 (2), p.76
Main Authors: Lee, Yang-Hi, Kim, Gwang
Format: Article
Language:English
Subjects:
additive (Cauchy) equation
additive mapping
Banach spaces
Functional equations
generalized Hyers–Ulam stability
Hyers–Ulam stability
hyperstability
Inequality
Stability
Theorems
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Summary: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.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms8020076