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Hyers-Ulam stability of Fibonacci functional equation. (English) Zbl 1197.39017

Let X be a real vector space. A function f:X is called a Fibonacci function if it satisfies the equation

f(x)=f(x-1)+f(x-2)forallx·

The author investigates the Hyers-Ulam stability of the equation above. He also proves that the general solution of the Fibonacci functional equation is related to the Fibonacci numbers F n where, F n =F n-1 +F n-2 for all n2 and F(0)=1,F(1)=1.

MSC:
39B82Stability, separation, extension, and related topics
39B22Functional equations for real functions
11B39Fibonacci and Lucas numbers, etc.