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진선숙,이양희 영남수학회 2020 East Asian mathematical journal Vol.36 No.1
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.
Jin, Sun-Sook,Lee, Yang-Hi The Youngnam Mathematical Society 2020 East Asian mathematical journal Vol.36 No.1
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.
A FIXED POINT APPROACH TO THE STABILITY OF AN ADDITIVE-QUADRATIC-QUARTIC FUNCTIONAL EQUATION
이양희 충청수학회 2020 충청수학회지 Vol.33 No.1
In this paper, we investigate the stability of a functional equation \begin{align*}& f(x+3y) -5 f(x+2y) +10f(x+y) - 8f(x) + 5f(x-y) - f(x-2y)\\ & -2f(-x)-f(2x)+f(-2x) = 0 \end{align*} by using the fixed point theory in the sense of L. C\u adariu and V. Radu.
HYERS-ULAM-RASSIAS STABILITY OF AN ADDITIVE-QUADRATIC-QUARTIC FUNCTIONAL EQUATION
Lee, Yang-Hi The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.4
In this paper, we investigate Hyers-Ulam-Rassias stability of a functional equation f(x + ky) + f(x - ky) - k<sup>2</sup>f(x + y) - k<sup>2</sup>f(x - y) + 2(k<sup>2</sup> - 1)f(x) + (k<sup>2</sup> + k)f(y) + (k<sup>2</sup> - k)f(-y) - 2f(ky) = 0.
Hyers-Ulam-Rassias stability of an additive-quadratic-quartic functional equation
Yang-Hi Lee 호남수학회 2019 호남수학학술지 Vol.41 No.4
In this paper, we investigate Hyers-Ulam-Rassias stability of a functional equation \begin{align*} f(x +ky)& + f(x-ky) - k^2f(x+y) - k^2f(x-y) +2(k^2-1)f(x)\nonumber \\ &\ + (k^2+k)f(y)+ (k^2-k)f(-y)-2f(ky)=0. \end{align*}
On the Hyers-Ulam-Rassias Stability of an Additive-cubic-quartic Functional Equation
이양희 한국수학교육학회 2019 純粹 및 應用數學 Vol.26 No.4
In this paper, we investigate Hyers-Ulam-Rassias stability of the functional equation \begin{align*} f(x+ky) & - k^2 f(x+y)+2(k^2-1)f(x)- k^2 f(x-y)+ f(x-ky)\nonumber \\ & - k^2(k^2 -1)(f(y) + f(-y))=0. %\\ f(x+2y) & - 4 f(x+y)+ 6f(x)- 4 f(x-y)+ f(x-2y)\nonumber % \\ & - f(2y)-f(-2y) + 4 f(y)+ 4 f(-y)=0, \end{align*} where $k$ is a fixed real number with $k \not\in \{ 0, 1,-1 \}$
A FIXED POINT APPROACH TO THE STABILITY OF AN ADDITIVE-QUADRATIC-QUARTIC FUNCTIONAL EQUATION
Yang-Hi Lee 충청수학회 2020 충청수학회지 Vol.33 No.1
In this paper, we investigate the stability of a functional equation
ON THE GENERAL SOLUTION OF A QUARTIC FUNCTIONAL EQUATION
Chung, Jukang-K.,Sahoo, Prasanna, K. Korean Mathematical Society 2003 대한수학회보 Vol.40 No.4
In this paper, we determine the general solution of the quartic equation f(x+2y)+f(x-2y)+6f(x) = 4[f(x+y)+f(x-y)+6f(y)] for all x, $y\;\in\;\mathbb{R}$ without assuming any regularity conditions on the unknown function f. The method used for solving this quartic functional equation is elementary but exploits an important result due to M. Hosszu [3]. The solution of this functional equation is also determined in certain commutative groups using two important results due to L. Szekelyhidi [5].
Sun-Sook Jin,Yang-Hi Lee 경남대학교 수학교육과 2020 Nonlinear Functional Analysis and Applications Vol.25 No.2
In this paper, we prove the stability of functional equations related to an additivequartic mapping by using the fixed-point theory, which L. C ˘adariu and V. Radu used as away to prove the stability of functional equations.