• Kyungpook Mathematical Journal
• /
• 제53권3호
• /
• pp.419-433
• /
• 2013

In this paper, we prove the generalized Hyers-Ulam-Rassias stability for a system of functional equations, called general system of nonlinear functional equations, in non-Archimedean normed spaces and Menger probabilistic non-Archimedean normed spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제13권3호
• /
• pp.237-247
• /
• 2006

In this paper we solve the Hyers-Ulam stability problem for quadratic functional equations on restricted domains, and then obtain an asymptotic behavior of quadratic mappings on restricted domains.

• 대한수학회논문집
• /
• 제24권1호
• /
• pp.5-16
• /
• 2009

In this paper, we obtain the general solution and the generalized Hyers-Ulam-Rassias stability for a following functional equation $$\sum\limits_{i=1}^mf(x_i+\frac{1}{m}\sum\limits_{{i=1\atop j{\neq}i}\.}^mx_j)+f(\frac{1}{m}\sum\limits_{i=1}^mx_i)=2f(\sum\limits_{i=1}^mx_i)$$ for a fixed positive integer m with $m\;{\geq}\;2$. This is applied to investigate derivations and their stability on proper Lie $CQ^*$-algebras. The concept of Hyers-Ulam-Rassias stability originated from the Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978), 297-300.

• 대한수학회보
• /
• 제44권3호
• /
• pp.569-587
• /
• 2007

In this paper, we establish the generalized Hyers-Ulam-Rassias stability of the Pexider type quadratic equation $f_1(x+y+z)+f_2(x-y)+f_3(x-z)-f_4(x-y-z)-f_5(x+y)-f_6(x+z)=0$ and its general solution.

• 충청수학회지
• /
• 제26권4호
• /
• pp.907-913
• /
• 2013

In this paper, we prove the generalized Hyers-Ulam stability of the additive functional inequality $${\parallel}f(2x_1)+f(2x_2)+{\cdots}+f(2x_n){\parallel}{\leq}{\parallel}tf(x_1+x_2+{\cdots}+x_n){\parallel}$$ in Banach spaces where a positive integer $n{\geq}3$ and a real number t such that 2${\leq}$t

• 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.

• East Asian mathematical journal
• /
• 제34권5호
• /
• pp.693-702
• /
• 2018

In this paper, we consider the generalized Hyers-Ulam stability for the following additive-quadratic functional equation with involution $f(x+2y)-f(2x+y)+f(x+y)+f({\sigma}(x)+y)+f(x)-4f(y)-f({\sigma}(y))=0$ in non-Archimedean spaces.

• Journal of applied mathematics & informatics
• /
• 제32권5_6호
• /
• pp.817-825
• /
• 2014

In this paper, we prove the generalized Hyers-Ulam stability of the following cubic funtional equation f(2x + y) + f(2x - y) = 2f(x + 2y) - 4f(x + y) + 18f(x) - 12f(y) by the direct method in 2-normed spaces.

• East Asian mathematical journal
• /
• 제31권5호
• /
• pp.627-634
• /
• 2015

In this paper, we investigate the following orthogonally additive-quadratic functional equation f(2x + y) - f(x + 2y) - f(x + y) - f(y - x) - f(x) + f(y) + f(2y) = 0. and prove the generalized Hyers-Ulam stability for it in orthogonality spaces by using the fixed point method.

• 충청수학회지
• /
• 제28권2호
• /
• pp.321-330
• /
• 2015

In this paper, we prove the generalized Hyers-Ulam stability for the following additive-quadratic functional equation f(2x + y) + f(2x - y) = f(x + y) + f(x - y) + 4f(x) + 2f(-x) in modular spaces by using a fixed point theorem for modular spaces.