• 대한수학회논문집
• /
• 제16권2호
• /
• 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.

• 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
• /
• 제31권1호
• /
• pp.89-101
• /
• 2018

In this paper, we consider the Hyers-Ulam stability on multi-valued dynamics. For a generalized n-dimensional quadratic set-valued functional equation, we prove the Hyers-Ulam stability for the functional equation in multi-valued dynamics.

• 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.

• 충청수학회지
• /
• 제20권2호
• /
• pp.117-137
• /
• 2007

We establish the Hyers-Ulam-Rassias stability of the Pexiderized mixed type quadratic equation $f_1(x+y+z)+f_2(x-y)+f_3(x-z)-f_4(x-y-z)-f_5(x+y)-f_6(x+z)=0$ in the spirit of D. H. Hyers, S. M. Ulam and Th. M. Rassias.

• 대한수학회지
• /
• 제38권3호
• /
• pp.645-656
• /
• 2001

In this paper, we will prove the Hyers-Ulam stability of the quadratic functional equation of Pexider type, f$_1$(x+y) + F$_2$(x-y) = f$_3$(x) + f$_4$(y).

• 대한수학회논문집
• /
• 제23권4호
• /
• pp.567-575
• /
• 2008

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

• Journal of applied mathematics & informatics
• /
• 제13권1_2호
• /
• pp.471-477
• /
• 2003

In this paper we invstigate the new additive type functional equation f(2x - y) + f(x-2y) = 3f(x)-3f(y) and prove the stability problem for this equation in the spirit of Hyers, Ulam, Rassias and Gavruta.

• 충청수학회지
• /
• 제29권1호
• /
• pp.83-93
• /
• 2016

In this paper, we introduce a generalized quadratic functional equation with several variables and then investigate its generalized Hyers-Ulam stability in normed spaces.

• Kyungpook Mathematical Journal
• /
• 제55권1호
• /
• pp.103-107
• /
• 2015

In this paper, we investigate the stability of Pompeiu's points in the sense of Hyers-Ulam.