• The Pure and Applied Mathematics
• /
• v.17 no.4
• /
• pp.373-388
• /
• 2010

We introduce mixed cubic-quartic functional equations. And using the fixed point method, we prove the generalized Hyers-Ulam stability of cubic-quartic functional equations on random normed spaces.

• Communications of the Korean Mathematical Society
• /
• v.20 no.2
• /
• pp.321-338
• /
• 2005

In this paper we investigate a generalization of the Hyers-Ulam-Rassias stability for a functional equation of the form $f(\varphi(X))\;=\;\phi(X)f(X)$, where X lie in n-variables. As a consequence, we obtain a stability result in the sense of Hyers, Ulam, Rassias, and Gavruta for many other equations such as the gamma, beta, Schroder, iterative, and G-function type's equations.

• Communications of the Korean Mathematical Society
• /
• v.23 no.4
• /
• pp.567-575
• /
• 2008

In this article we prove the Hyers.Ulam stability of trigonometric functional equations.

• Honam Mathematical Journal
• /
• v.29 no.1
• /
• pp.61-74
• /
• 2007

Th. M. Rassias obtained the Hyers-Ulam stability of the general Euler-Lagrange functional equation. In this paper we prove the stability of generlized Euler-Lagrange functional equations in the spirit of Hyers, Ulam, Rassias and G$\breve{a}$vruta.

• Communications of the Korean Mathematical Society
• /
• v.16 no.4
• /
• pp.607-619
• /
• 2001

Rassias obtained the Hyers-Ulam stability of the gen-eral Euler-Lagrange functional equation. In this paper we general-ized this stability in the spirit of Hyers, Ulam, Rassias and Gavruta.

• Communications of the Korean Mathematical Society
• /
• v.20 no.1
• /
• pp.93-106
• /
• 2005

In this paper, we obtain the generalization of the Hyers-Ulam-Rassias stability in the sense of Gavruta and Ger of the generalized G-type functional equations of the form $f({{\varphi}(x)) = {\Gamma}(x)f(x)$. As a consequence in the cases ${\varphi}(x) := x+p:= x+1$, we obtain the stability theorem of G-functional equation : the reciprocal functional equation of the double gamma function.

• Kyungpook Mathematical Journal
• /
• v.60 no.1
• /
• pp.133-144
• /
• 2020

We will prove the generalized Hyers-Ulam stability of cubic-quadratic-additive type functional equations and general cubic functional equations whose solutions are cubic-quadratic-additive mappings and general cubic mappings, respectively.

• Journal of applied mathematics & informatics
• /
• v.14 no.1_2
• /
• pp.429-445
• /
• 2004

In this paper we investigate the generalized Hyers-Ulam-Rassias stability for a functional equation of the form $f(\varphi(x,y)){\;}={\;}\phi(x,y)f(x,y)$, where x, y lie in the set S. As a consequence we obtain stability in the sense of Hyers, Ulam, Rassias, Gavruta, for some well-known equations such as the gamma, beta and G-function type equations.

• Communications of the Korean Mathematical Society
• /
• v.15 no.1
• /
• pp.45-50
• /
• 2000

The modified Hyers-Ulam-Rassias Stability Of the generalized form g(x+p) : $\phi$(x)g(x) for the Gamma functional equation shall be proved. As a consequence we obtain the stability theorems for the gamma functional equation.

• Communications of the Korean Mathematical Society
• /
• v.16 no.2
• /
• pp.211-223
• /
• 2001

In this paper, we obtain the modified Hyers-Ulam-Rassias stability for the family of the functional equation f(x o y) = H(f(x)(sup)1/t, f(y)(sup)1/t)(x,y) $\in$S), where H is a s homogeneous function of degree t and o is a square-symmetric operation on the set S.