• Journal of the Chungcheong Mathematical Society
• /
• v.15 no.1
• /
• pp.35-41
• /
• 2002

In this paper, we prove the stability of a Jensen's functional equation on a normed almost linear space.

• Journal of the Chungcheong Mathematical Society
• /
• v.14 no.2
• /
• pp.1-7
• /
• 2001

In this paper we prove the stability of some generaliged quadratic functional equation $$a^2f(\frac{x+y}{a})+a^2f(\frac{x-y}{a})=2f(x)+2f(y)$$.

• Honam Mathematical Journal
• /
• v.29 no.4
• /
• pp.543-554
• /
• 2007

In this paper, we prove the stability of a mixed type functional equation f( -x + y + z) + f(x - y + z) + f(x + y - z) = f(x - y) + f(y - z) + f(z - x) + f.(x) + f(y) + f(z).

• The Pure and Applied Mathematics
• /
• v.27 no.1
• /
• pp.51-60
• /
• 2020

In this note, we investigate the Hyers-Ulam stability and the hyperstability of the Pexider type functional equation g(x + y + xy) = g(x) + f(y) + xf(y) + yg(x).

• East Asian mathematical journal
• /
• v.35 no.3
• /
• pp.331-340
• /
• 2019

In this paper, we investigate the stability for the functional equation $f(x+ky)-kf(x+y)+kf(x-y)-f(x-ky)-(k^3-k)f(y)+(k^3-k)f(-y)=0$ in the sense of M. S. Moslehian and Th. M. Rassias.

• The Pure and Applied Mathematics
• /
• v.28 no.1
• /
• pp.15-26
• /
• 2021

The purpose of this paper is to introduce a new type of a cubic functional equation and then investigate its stability problems in a convex modular space with a generalized ∆a-condition.

• The Pure and Applied Mathematics
• /
• v.15 no.2
• /
• pp.169-178
• /
• 2008

In this paper we generalize the superstability of the exponential functional equation proved by J. Baker et al. [2], that is, we solve an exponential type functional equation $$f(x+y)\;=\;a^{xy}f(x)f(y)$$ and obtain the superstability of this equation. Also we generalize the stability of the exponential type equation in the spirt of R. Ger[4] of the following setting $$|{\frac{f(x\;+\;y)}{{a^{xy}f(x)f(y)}}}\;-\;1|\;{\leq}\;{\delta}.$$

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.3
• /
• pp.801-813
• /
• 2019

In this paper, using the Baire category theorem we investigate the Hyers-Ulam stability problem of pexiderized Jensen functional equation $$2f(\frac{x+y}{2})-g(x)-h(y)=0$$ and pexiderized Jensen type functional equations $$f(x+y)+g(x-y)-2h(x)=0,\\f(x+y)-g(x-y)-2h(y)=0$$ on a set of Lebesgue measure zero. As a consequence, we obtain asymptotic behaviors of the functional equations.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.4
• /
• pp.887-900
• /
• 2013

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

• Kyungpook Mathematical Journal
• /
• v.50 no.4
• /
• pp.557-564
• /
• 2010

By using an idea of C$\u{a}$dariu and Radu [4], we prove the generalized Hyers-Ulam stability of the functional equation f(x + y,z - w) + f(x - y,z + w) = 2f(x, z) + 2f(y, w). The quadratic form $f\;:\;\mathbb{R}\;{\times}\;\mathbb{R}{\rightarrow}\mathbb{R}$ given by f(x, y) = $ax^2\;+\;by^2$ is a solution of the above functional equation.