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

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  • Soon-Mo Jung
  • Michael Th. Rassias

Abstract

Given a vector space X, we investigate the solutions f:R→X of the linear functional equation of third order f(x) = pf(x − 1) + qf(x − 2) + rf(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.

Suggested Citation

  • Soon-Mo Jung & Michael Th. Rassias, 2014. "A Linear Functional Equation of Third Order Associated with the Fibonacci Numbers," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:137468
    DOI: 10.1155/2014/137468
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    References listed on IDEAS

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    1. Soon-Mo Jung, 2011. "Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis," Springer Optimization and Its Applications, Springer, number 978-1-4419-9637-4, January.
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    Cited by:

    1. Cristinel Mortici & Michael Th. Rassias & Soon-Mo Jung, 2014. "On the Stability of a Functional Equation Associated with the Fibonacci Numbers," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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