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Stability of an additive-quadratic-quartic functional equation

Kim Gwang Hui, Lee Yang-Hi

Demonstratio Mathematica

2020

Vol. 53, nr 1

1--7

In this paper, we investigate the stability of an additive-quadratic-quartic functional equation f(x+2y)+f(x-2y) - 2f(x+y) - 2f(-x-y) - 2f(x-y) - 2f(y-x)+4f(-x)+2f(x) - f(2y) - f(-2y)+4f(y)+4f(-y)=0 by the direct method in the sense of Găvruta.

Stability and hyperstability of a quadratic functional equation and a characterization of inner product spaces

EL-Fassi I., Park C., Kim G. H.

Demonstratio Mathematica

2018

Vol. 51, nr 1

295--303

We have proved the Hyers-Ulam stability and the hyperstability of the quadratic functional equation f(x+y+z) +f(x+y−z) +f(x−y+z) +f(−x+y+z) = 4[f(x) +f(y) +f(z) ] in the class of functions from an abelian group G into a Banach space.

On the stability of a Cauchy type functional equation

Najati A., Lee J. R., Park C., Rassias T. M.

Demonstratio Mathematica

2018

Vol. 51, nr 1

323--331

In this work, the Hyers-Ulam type stability and the hyperstability of the functional equation [wzór] are proved.