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Jung, Soon-Mo; Rassias, Michael Th.

A linear functional equation of third order associated with the Fibonacci numbers. (English) Zbl 1470.39066

Abstr. Appl. Anal. 2014, Article ID 137468, 7 p. (2014).
Summary: Given a vector space \(X\), we investigate the solutions \(f : \mathbb{R} \rightarrow X\) of the linear functional equation of third order \(f \left(x\right) = p f \left(x - 1\right) + q f \left(x - 2\right) + r f(x - 3)\), which is strongly associated with a well-known identity for the Fibonacci numbers. Moreover, we prove the Hyers-Ulam stability of that equation.

Cited in 28 Documents

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
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References:

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