On solution and stability of functional equation $f(x+y)^2=af(x)f(y)+bf(x)^2+cf(y)^2$

Abstract

The general (continuous) solution and the asymptotic behaviors of the unbounded solution of the functional equation $f(x + y)^2 = af(x)f(y) + bf(x)^2 + cf(y)^2$ and the Hyers-Ulam stability of that functional equation for the case when a = 2 and b = c = 1 shall be investigated.

Keywords

• Functional equation;
• Hyers-Ulam stability

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References

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2. Proc. Nat. Acad. Sci. U.S.A. v.27 On the stability of the linear functional equation D.H. Hyers
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