The stability of the sine equation
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- by Piotr W. Cholewa PDF
- Proc. Amer. Math. Soc. 88 (1983), 631-634 Request permission
Abstract:
Let $\delta$ be a positive real constant and let $G$ be an abelian group (written additively) in which division by 2 is uniquely performable. Every unbounded complex-valued function $f$ on $G$ satisfying the inequality \[ \left | {f(x + y)f(x - y) - f{{(x)}^2} + f{{(y)}^2}} \right | \leqslant \delta \quad {\text {for all }}x,y \in G\] has to be a solution of the sine functional equation \[ f(x + y)f(x - y) = f{(x)^2} - f{(y)^2}\quad {\text {for all }}x,y \in G.\]References
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Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 88 (1983), 631-634
- MSC: Primary 39B20
- DOI: https://doi.org/10.1090/S0002-9939-1983-0702289-8
- MathSciNet review: 702289