• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제26권4호
• /
• pp.247-254
• /
• 2019

In this paper, we investigate Hyers-Ulam-Rassias stability of the functional equation f(x + ky) - k²f(x + y) + 2(k² - 1)f(x) - k²f(x - y) + f(x - ky) - k²(k² - 1)(f(y) + f(-y)) = 0, where k is a fixed real number with |k| ≠ 0, 1.

• 한국수학사학회지
• /
• 제17권1호
• /
• pp.61-68
• /
• 2004

This paper aims at investigating the algebraic solution of cubic and quartic equation and eliciting the didactical meanings of them. First, I examine the event which relates to the equation in the history of mathematics and investigate the algebraic solution of cubic and quartic equation. And then I elicit the didactical suggestions which are required of teachers and students when they investigate the algebraic solution of cubic and quartic equation. In general, the investigation of these solutions is the valuable task which requires the algebraic intuition and technique for students and certificates expert knowledge for teachers.

• Korean Journal of Mathematics
• /
• 제28권2호
• /
• pp.159-168
• /
• 2020

In this paper, we investigate Hyers-Ulam-Rassias stability of a functional equation f(x + ky) + f(x - ky) - k²f(x + y) - k²f(x - y) + 2(k² - 1)f(x) + (k² + k³)f(y) + (k² - k³)f(-y) - 2f(ky) = 0.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제15권2호
• /
• pp.103-110
• /
• 2008

In this paper, we obtain the general solution and the stability of the cubic functional equation f(2x + y, 2z + w) + f(2x - y, 2z - w) = 2f(x + y, z + w) + 2f(x - y, z - w) + 12f(x, z). The cubic form $f(x,\;y)\;=\;ax^3\;+\;bx^2y\;+\;cxy^2\;+\;dy^3$ is a solution of the above functional equation.

• 충청수학회지
• /
• 제32권3호
• /
• pp.295-307
• /
• 2019

In this paper, we investigate Hyers-Ulam-Rassias stability of the functional equation $$f(x+ky)-{\frac{k^2+k}{2}}f(x+y)+(k^2-1)f(x)-{\frac{k^2-k}{2}}f(x-y)\\{\hfill{67}}-f(ky)+{\frac{k^2+k}{2}}f(y)+{\frac{k^2-k}{2}}f(-y)=0.$$

• 충청수학회지
• /
• 제32권1호
• /
• pp.29-46
• /
• 2019

We introduce a generalized cubic functional equation and investigate the Hyers-Ulam stability of the cubic functions as solutions to the generalized cubic functional equation on a quasi-fuzzy anti-${\beta}$-Banach space by both the direct method and the fixed point method.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제26권4호
• /
• pp.267-276
• /
• 2019

In this paper, we investigate the stability of an additive-cubic-quartic functional equation f(x + 2y) - 4f(x + y) + 6f(x) - 4f(x - y) + f(x - 2y) - 12f(y) - 12f(-y) = 0 by applying the fixed point theory in the sense of L. Cădariu and V. Radu.

• 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.

• 대한수학회보
• /
• 제44권4호
• /
• pp.825-840
• /
• 2007

In this paper, we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability problem for the following cubic functional equation 3f(x+3y)+f(3x-y)=15f(x+y)+15f(x-y)+80f(y). The concept of Hyers-Ulam-Rassias stability originated from 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.

• 충청수학회지
• /
• 제24권4호
• /
• pp.703-712
• /
• 2011

In this paper, we investigate the stability of a cubic functional equation $$f(x+ny)+f(x-ny)+f(nx)=n^2f(x+y)+n^2f(x-y)+(n^3-2n^2+2)f(x)$$ in p-Banach spaces and in Banach modules, where $n{\geq}2$ is an integer.