• Korean Journal of Mathematics
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• v.28 no.2
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• pp.159-168
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.253-267
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• 2003

In this paper we deal With the quadratic functional equation (equation omitted) deriving from an inequality of T. Popoviciu for convex functions. We solve this functional equation by proving that its solutions we the polynomials of degree at most two. Likewise, we investigate its stability in the spirit of Hyers, Ulam, and Rassias.

• Honam Mathematical Journal
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• v.29 no.2
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• pp.193-204
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• 2007

In this paper, we investigate some results concerning the stability of the following quadratic type functional equation: f(x + y) + f(x - y) + f(y + z) + f(y - z) + f(z + x) + f(z - x) = 4f(x) + 4f(y) + 4f(z).

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.377-392
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• 2004

In the present paper, we obtain the Hyers-Ulam-Rassias stability in the sense of Gavruta for the general quadratic functional equation f(χ + y + z) + f(χ - y) + f(χ - z) = f(χ - y - z) + f(χ + y) + f(χ + z).

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.435-446
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• 2004

In this paper, we obtain the general solution of a quadratic functional equation $b^2f(\frac{x+y+z}{b})+f(x-y)+f(x-z)=\;a^2[f(\frac{x-y-z}{a})+f(\frac{x+y}{a})+f(\frac{x+z}{a})]$ and prove the stability of this equation.

• The Pure and Applied Mathematics
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• v.11 no.4
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• pp.323-335
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• 2004

In this paper, we solve the general solution of a modified additive and quadratic functional equation f(χ + 3y) + 3f(χ-y) = f(χ-3y) + 3f(χ+y) in the class of functions between real vector spaces and obtain the Hyers-Ulam-Rassias stability problem for the equation in the sense of Gavruta.

• Honam Mathematical Journal
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• v.41 no.4
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• pp.813-821
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• 2019

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 + k)f(y) + (k² - k)f(-y) - 2f(ky) = 0.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.321-330
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• 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.

• Communications of the Korean Mathematical Society
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• v.16 no.1
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• pp.103-111
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• 2001

In this paper, we investigate a generalization of the stability of a new quadratic functional equation f(∑(sub)i=1(sup)n x(sub)i)+∑(sub)1$\leq$i$\leq$n f(x(sub)i-x(sub)j) = n∑(sub)i=1(sup)n f(x(sub)i) (n$\geq$2) in the spirits of Hyers, Ulam, Rassias and Gavruta.

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.477-493
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• 2004

In this paper we prove the solution and stability of the quadratic type functional equations with two variables $4f(\frac{x-2y}{2}) + f(x) + 2f(y)= 8f(\frac{x-y}{2})+ f(2y)$ and f(x-2y)+f(x)+sf(y)-2f(x-y)+f(2y).