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A Note on Stability of an Operator Linear Equation of the Second Order

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  • Janusz Brzdȩk
  • Soon-Mo Jung

Abstract

We prove some Hyers‐Ulam stability results for an operator linear equation of the second order that is patterned on the difference equation, which defines the Lucas sequences (and in particular the Fibonacci numbers). In this way, we obtain several results on stability of some linear functional and differential and integral equations of the second order and some fixed point results for a particular (not necessarily linear) operator.

Suggested Citation

  • Janusz Brzdȩk & Soon-Mo Jung, 2011. "A Note on Stability of an Operator Linear Equation of the Second Order," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:602713
    DOI: 10.1155/2011/602713
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    References listed on IDEAS

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    1. Stević, Stevo, 2008. "Bounded solutions of a class of difference equations in Banach spaces producing controlled chaos," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 238-245.
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    Cited by:

    1. Nicole Brillouët-Belluot & Janusz Brzdęk & Krzysztof Ciepliński, 2012. "On Some Recent Developments in Ulam′s Type Stability," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. M. Eshaghi Gordji & H. Khodaei & Y. W. Lee & G. H. Kim, 2012. "Approximation of Mixed‐Type Functional Equations in Menger PN‐Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).

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