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Ulam Stability of a Quartic Functional Equation

Author

Listed:
  • Abasalt Bodaghi
  • Idham Arif Alias
  • Mohammad Hosein Ghahramani

Abstract

The oldest quartic functional equation was introduced by J. M. Rassias in (1999), and then was employed by other authors. The functional equation 𠑓 ( 2 𠑥 + 𠑦 ) + 𠑓 ( 2 𠑥 − 𠑦 ) = 4 𠑓 ( 𠑥 + 𠑦 ) + 4 𠑓 ( 𠑥 − 𠑦 ) + 2 4 𠑓 ( 𠑥 ) − 6 𠑓 ( 𠑦 ) is called a quartic functional equation, all of its solution is said to be a quartic function . In the current paper, the Hyers-Ulam stability and the superstability for quartic functional equations are established by using the fixed-point alternative theorem.

Suggested Citation

  • Abasalt Bodaghi & Idham Arif Alias & Mohammad Hosein Ghahramani, 2012. "Ulam Stability of a Quartic Functional Equation," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-9, April.
    • Handle: RePEc:hin:jnlaaa:232630
    DOI: 10.1155/2012/232630
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