A Linear Functional Equation of Third Order Associated with the Fibonacci Numbers

الملخص EN

Given a vector space X , we investigate the solutions f : R → X of the linear functional equation of third order f x = p f x - 1 + q f x - 2 + 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.