• Journal of the Chungcheong Mathematical Society
• /
• v.15 no.2
• /
• pp.73-84
• /
• 2003

In this paper, we investigate the new quadratic type functional equation f(2x + y) - f(x + 2y) = 3f(x) - 3f(y) and prove the stablility of this equation in the spirit of Hyers, Ulam, Rassias and G$\breve{a}$vruţa.

• Journal of applied mathematics & informatics
• /
• v.8 no.2
• /
• pp.561-567
• /
• 2001

In this paper, we investigate the Hyers-Ulam-Rassias stability of a quadratic functional equation f(x+y+z)+f(x-y)+f(y-z)+f(x-z) = 3f(x)+3f(y)+3f(z) and prove the Hyers-Ulam stability of the equation on bounded domains.

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.261-272
• /
• 2001

In this paper we prove the stability of the generalized quadratic equation f(x+y)+g(x-y)-2f(x)-2g(y)=0 in the spirit of Hyers, Ulam and Rassias.

• Korean Journal of Mathematics
• /
• v.20 no.1
• /
• pp.77-89
• /
• 2012

Using fixed point method, we prove the Hyers-Ulam stability of the orthogonally additive functional equation (0.1) $f(2x+y)=2f(x)+f(y)$ and of the orthogonally quadratic functional equation (0.2) $2f(\frac{x}{2}+y)+2f(\frac{x}{2}-y)=f(x)+4f(y)$ for all $x$, $y$ with $x{\perp}y$ in orthogonality spaces.

• Communications of the Korean Mathematical Society
• /
• v.27 no.3
• /
• pp.523-535
• /
• 2012

In this paper, we investigate a fuzzy version of stability for the functional equation $$2f(x+y)+f(x-y)+f(y-x)-3f(x)-f(-x)-3f(y)-f(-y)=0$$ in the sense of M. Mirmostafaee and M. S. Moslehian.

• Journal of applied mathematics & informatics
• /
• v.15 no.1_2
• /
• pp.377-392
• /
• 2004

In the present paper, we obtain the Hyers-Ulam-Rassias stability in the sense of Gavruta for the general quadratic functional equation f(χ + y + z) + f(χ - y) + f(χ - z) = f(χ - y - z) + f(χ + y) + f(χ + z).

• Journal of applied mathematics & informatics
• /
• v.9 no.1
• /
• pp.415-421
• /
• 2002

We extend the Hyers-Ulsam-Rassias stability of a quadratic functional equation f(χ+y+z)+f(χ-y)+f(y-Z)+f(χ-z) = 3f(χ)+3f(y)+3f(z) to Banach modules over a Banach algebra.

• Journal of the Chungcheong Mathematical Society
• /
• v.33 no.1
• /
• pp.77-87
• /
• 2020

In this paper, we investigate the stability of a functional equation f(x + 3y) - 5f(x + 2y) + 10f(x + y) - 8f(x) + 5f(x - y) - f(x - 2y) - 2f(-x) - f(2x) + f(-2x) = 0 by using the fixed point theory in the sense of L. Cǎdariu and V. Radu.

• East Asian mathematical journal
• /
• v.35 no.5
• /
• pp.559-568
• /
• 2019

In this paper, we investigate the stability problems for a functional equation f(x + 2y)+f(x - 2y) - 4f(x + y) - 4f(x - y) + 6f(x) - 2f(2y) + 12f(y) - 4f(-y) = 0 by using the fixed point theory in the sense of L. C˘adariu and V. Radu.

• The Pure and Applied Mathematics
• /
• v.26 no.1
• /
• pp.49-58
• /
• 2019

In this paper, I prove the stability problem for a quadratic-cubic functional equation $$f(x+ky)-k^2f(x+y)-k^2f(x-y)+f(x-ky)+f(kx)-{\frac{k^3-3k^2+4}{2}}f(x)+{\frac{k^3-k^2}{2}}f(-x)=0$$ in modular spaces by applying the direct method.