The stability of the sine equation. (English) Zbl 0547.39003

The author considers the stability problem for the sine equation. Let G be an abelian group in which division by 2 is uniquely performed. It is shown that every unbounded complex-valued function f on G is a solution of the sine functional equation \(f(x+y)f(x-y)=f(x)^ 2-f(y)^ 2\) for all x,\(y\in G\) if f satisfies the inequality \(| f(x+y)f(x-y)-f(x)^ 2+f(y)^ 2|\leq \delta\) for all x,\(y\in G\) where \(\delta\) is a positive real constant.
Reviewer: G.Dial


39B52 Functional equations for functions with more general domains and/or ranges
39B99 Functional equations and inequalities
39B72 Systems of functional equations and inequalities
Full Text: DOI


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