• Journal of applied mathematics & informatics
• /
• v.9 no.1
• /
• pp.389-399
• /
• 2002

In this paper we solve a quadratic Jensen type functional equation (equation omitted) and prove the stability of this equation.

• Journal of applied mathematics & informatics
• /
• v.15 no.1_2
• /
• pp.447-456
• /
• 2004

In this paper we investigate the Hyers-Ulam-Rassias stability of a 4-dimensional quadratic functional equation (equation omitted).

• East Asian mathematical journal
• /
• v.36 no.1
• /
• pp.35-53
• /
• 2020

In this paper, we investigate Hyers-Ulam-Rassias stability of an additive-quartic functional equation, of a quadratic-quartic functional equation, and of a cubic-quartic functional equation.

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.2
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.3
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.2
• /
• pp.183-193
• /
• 2003

In this Paper, we Prove the stability Of E quadratic type functional equation (equation omitted).

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.3
• /
• 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.

• Korean Journal of Mathematics
• /
• v.23 no.3
• /
• pp.393-399
• /
• 2015

W. Park [J. Math. Anal. Appl. 376 (2011) 193-202] proved the Hyers-Ulam stability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces. But there are serious problems in the control functions given in all theorems of the paper. In this paper, we correct the statements of these results and prove the corrected theorems. Moreover, we prove the superstability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces under the original given conditions.

• The Mathematical Education
• /
• v.57 no.3
• /
• pp.231-246
• /
• 2018

In this paper, we applied Sfard's reification theory to analyze the secondary students' level of conceptualization with regard to the formula of quadratic equation. Through the generation and development of mathematical concepts from a historical perspective, Sfard classified the formulation process into three stages of interiorization, condensation, and reification, and proposed levels of formulation. Based on this theory, we constructed a test tool reflecting the reversibility of the nature of manipulation of Piaget's theory as a criterion of content judgement in order to grasp students' conceptualization level of the formula of quadratic equation. By applying this tool, we analyzed the conceptualization level of the formula of quadratic equation of the $9^{th}$ and $10^{th}$ graders. The main results are as follows. First, approximately 45% of $9^{th}$ graders can not memorize the formula of quadratic equation, or even if they memorize, they do not have the ability of accurate calculation to apply for it. Second, high school curriculum requires for students to use the formula of the quadratic equation, but about 60% of $10^{th}$ graders have not reached at the level of reification that they can use the formula of quadratic equation. Third, as a result of imaginarily correcting the error of the previous concept, there was a change in the levels of $9^{th}$ graders, and there was no change in $10^{th}$ graders.

• Journal of the Korean Mathematical Society
• /
• v.38 no.3
• /
• 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).