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On the Generalized Ulam-Gavruta-Rassias Stability of Mixed-Type Linear and Euler-Lagrange-Rassias Functional Equations

Author

Listed:
  • Paisan Nakmahachalasint

Abstract

In this paper, the mixed-type linear and Euler-Lagrange-Rassias functional equations introduced by J. M. Rassias is generalized to the following n -dimensional functional equation: f ( ∑ i = 1 n x i ) + ( n − 2 ) ∑ i = 1 n f ( x i ) = ∑ 1 ≤ i < j ≤ n f ( x i − x j ) when n > 2 . We prove the general solutions and investigate its generalized Ulam-Gavruta-Rassias stability.

Suggested Citation

  • Paisan Nakmahachalasint, 2007. "On the Generalized Ulam-Gavruta-Rassias Stability of Mixed-Type Linear and Euler-Lagrange-Rassias Functional Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2007, pages 1-10, May.
    • Handle: RePEc:hin:jijmms:063239
    DOI: 10.1155/2007/63239
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    Cited by:

    1. M. Eshaghi Gordji & G. H. Kim, 2012. "Approximate n‐Lie Homomorphisms and Jordan n‐Lie Homomorphisms on n‐Lie Algebras," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. G. Zamani Eskandani & P. Găvruţa & Gwang Hui Kim, 2012. "On the Stability Problem in Fuzzy Banach Space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. H. Azadi Kenary & H. Rezaei & S. Talebzadeh & S. Jin Lee, 2012. "Stabilities of Cubic Mappings in Various Normed Spaces: Direct and Fixed Point Methods," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. Choonkil Park & Won-Gil Park & Abbas Najati, 2009. "Functional Equations Related to Inner Product Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    5. Fridoun Moradlou & Hamid Vaezi & Choonkil Park, 2008. "Fixed Points and Stability of an Additive Functional Equation of n‐Apollonius Type in C∗‐Algebras," Abstract and Applied Analysis, John Wiley & Sons, vol. 2008(1).
    6. M. Janfada & R. Shourvazi, 2011. "Solutions and the Generalized Hyers‐Ulam‐Rassias Stability of a Generalized Quadratic‐Additive Functional Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    7. Yang-Hi Lee, 2014. "On the Generalized Hyers‐Ulam Stability of an n‐Dimensional Quadratic and Additive Type Functional Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    8. M. Eshaghi Gordji & M. B. Ghaemi & G. H. Kim & Badrkhan Alizadeh, 2011. "Stability and Superstability of Generalized (θ, ϕ)‐Derivations in Non‐Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    9. Jaiok Roh & Ick-Soon Chang, 2008. "Functional Inequalities Associated with Additive Mappings," Abstract and Applied Analysis, John Wiley & Sons, vol. 2008(1).
    10. Abbas Najati & Choonkil Park & Jung Rye Lee, 2009. "Homomorphisms and Derivations in C∗‐Ternary Algebras," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).

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