Hyers-Ulam stability of an additive-quadratic functional equation





In this paper, we introduce the following \((a,b,c)\)-mixed type functional equation of the form

\(g(ax_1+bx_2+cx_3 )-g(-ax_1+bx_2+cx_3 ) + g(ax_1-bx_2+cx_3 )\)\(-g(ax_1+bx_2-cx_3 ) + 2a^2 [g(x_1 ) + g(-x_1)] + 2b^2 [g(x_2 ) + g(-x_2)] + \)\(2c^2 [g(x_3 ) + g(-x_3)]+a[g(x_1 ) - g(-x_1)]+ b[g(x_2 )-g(-x_2)] + \)  \(c[g(x_3 )-g(-x_3)]=4g(ax_1+cx_3 )+2g(-bx_2)+\)  \(2g(bx_2)\)

where \(a,b,c\) are positive integers with \(a>1\), and investigate the solution and the Hyers-Ulam stability of the above functional equation in Banach spaces by using two different methods.


Hyers-Ulam stability , mixed type functional equation , Banach space , fixed point
  • Vediyappan Govindan Department of Mathematics, Sri Vidya Mandir Arts & Science College, Katteri, India.
  • Choonkil Park Research Institute of Natural Sciences, Hanyang University, Seoul-04763, Korea.
  • Sandra Pinelas Departamento de Ciências Exatas e Engenharia, Academia Militar, Portugal.
  • Themistocles M. Rassias Department of Mathematics, National Technical University of Athens, Greece.
  • Pages: 233–255
  • Date Published: 2020-08-22
  • Vol. 22 No. 2 (2020)

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How to Cite

V. Govindan, C. Park, S. Pinelas, and T. M. Rassias, “Hyers-Ulam stability of an additive-quadratic functional equation”, CUBO, vol. 22, no. 2, pp. 233–255, Aug. 2020.