General solution and generalized Ulam-Hyers stability of a generalized n- type additive quadratic functional equation in Banach space and Banach algebra: direct and fixed point methods

  • Authors

    • S. Murthy GOVERNMENT ARTS COLLEGE,TIRUVANNAMALAI-606 603,TAMILNADU,INDIA.
    • M. Arunkumar Annai Veilankanni's College of Arts and Science,
    • V. Govindan GOVERNMENT ARTS COLLEGE,TIRUVANNAMALAI-606 603,TAMILNADU,INDIA.
    2015-05-19
    https://doi.org/10.14419/ijams.v3i1.4402
  • Additive Functional Equations, Quadratic Functional Equations, Mixed Type Functional Equations, Banach Space, Banach Algebra, Generalized Ulam-Hyers Stability, Fixed Point.

  • Abstract

    In this paper, the authors introduce and investigate the general solution and generalized Ulam-Hyers stability of a generalized n-type additive-quadratic functional equation.


    g(x + 2y; u + 2v) + g(x ô€€€ 2y; u ô€€€ 2v) = 4[g(x + y; u + v) + g(x ô€€€ y; u ô€€€ v)] ô€€€ 6g(x; u)
    + g(2y; 2v) + g(ô€€€2y;ô€€€2v) ô€€€ 4g(y; v) ô€€€ 4g(ô€€€y;ô€€€v)

    Where  is a positive integer with , in Banach Space and Banach Algebras using direct and fixed point methods.

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  • How to Cite

    Murthy, S., Arunkumar, M., & Govindan, V. (2015). General solution and generalized Ulam-Hyers stability of a generalized n- type additive quadratic functional equation in Banach space and Banach algebra: direct and fixed point methods. International Journal of Advanced Mathematical Sciences, 3(1), 25-64. https://doi.org/10.14419/ijams.v3i1.4402