• 대한수학회보
• /
• 제38권2호
• /
• 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.

• 대한수학회보
• /
• 제37권3호
• /
• pp.477-486
• /
• 2000

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(z-x)=3f(x)+3f(y)+3f(z) and prove the Hyers-Ulam stability of the equation on restricted (unbounded) domains.

• Kyungpook Mathematical Journal
• /
• 제49권4호
• /
• pp.691-700
• /
• 2009

We use the fixed alternative theorem to establish Hyers-Ulam-Rassias stability of the quadratic functional equation where functions map a linear space into a complete quasi p-normed space. Moreover, we will show that the continuity behavior of an approximately quadratic mapping, which is controlled by a suitable continuous function, implies the continuity of a unique quadratic function, which is a good approximation to the mapping. We also give a few applications of our results in some special cases.

• 대한수학회보
• /
• 제60권1호
• /
• pp.75-81
• /
• 2023

If a multiplicative function f is commutable with a quadratic form x² + xy + y², i.e., f(x² + xy + y²) = f(x)² + f(x) f(y) + f(y)², then f is the identity function. In other hand, if f is commutable with a quadratic form x² - xy + y², then f is one of three kinds of functions: the identity function, the constant function, and an indicator function for ℕ ＼ pℕ with a prime p.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제14권1호
• /
• pp.23-35
• /
• 2007

We investigate the modified Hyers-Ulam-Rassias stability for the following mixed type functional equation, i.e, cubic or quadratic type functional equation : 9f(x+y)-9f(x-y)+f(6y)=3f(x+3y)-3f(x-3y)+9f(2y).

• 대한수학회보
• /
• 제38권2호
• /
• pp.325-336
• /
• 2001

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

• 충청수학회지
• /
• 제17권1호
• /
• pp.57-75
• /
• 2004

The aim of this paper is to solve the general solution of a quadratic functional equation f(x + 2y) + 2f(x - y) = f(x - 2y) + 2f(x + y) in the class of functions between real vector spaces and to obtain the generalized Hyers-Ulam stability problem for the equation.

• 대한수학회보
• /
• 제42권1호
• /
• pp.133-148
• /
• 2005

In this paper, we obtain the general solution of a gen-eralized quadratic and additive type functional equation f(x + ay) + af(x - y) = f(x - ay) + af(x + y) for any integer a with a $\neq$ -1. 0, 1 in the class of functions between real vector spaces and investigate the generalized Hyers- Ulam stability problem for the equation.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제11권4호
• /
• pp.323-335
• /
• 2004

In this paper, we solve the general solution of a modified additive and quadratic functional equation f(χ + 3y) + 3f(χ-y) = f(χ-3y) + 3f(χ+y) in the class of functions between real vector spaces and obtain the Hyers-Ulam-Rassias stability problem for the equation in the sense of Gavruta.

• 호남수학학술지
• /
• 제38권4호
• /
• pp.693-699
• /
• 2016

The purpose of this note is to provide an alternative proof of two quadratic transformations contiguous to that of Kummer using a differential equation approach.