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

• The Pure and Applied Mathematics
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• v.29 no.2
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• pp.189-199
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• 2022

In this paper, we introduce a new generalized (a, b)-cubic Euler-Lagrange-Jensen functional equation and obtain its general solution. Furthermore, we prove the Hyers-Ulam stability of the new generalized (a, b)-cubic Euler-Lagrange-Jensen functional equation in orthogonality normed spaces.

• East Asian mathematical journal
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• v.35 no.3
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• pp.331-340
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• 2019

In this paper, we investigate the stability for the functional equation $f(x+ky)-kf(x+y)+kf(x-y)-f(x-ky)-(k^3-k)f(y)+(k^3-k)f(-y)=0$ in the sense of M. S. Moslehian and Th. M. Rassias.

• The Pure and Applied Mathematics
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• v.28 no.1
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• pp.15-26
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• 2021

The purpose of this paper is to introduce a new type of a cubic functional equation and then investigate its stability problems in a convex modular space with a generalized ∆a-condition.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.959-970
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• 2016

In this paper, we generalize the stability for an n-dimensional cubic functional equation in Banach space to set-valued dynamics. Let $n{\geq}2$ be an integer. We define the n-dimensional cubic set-valued functional equation given by $$f(2{{\sum}_{i=1}^{n-1}}x_i+x_n){\oplus}f(2{{\sum}_{i=1}^{n-1}}x_i-x_n){\oplus}4{{\sum}_{i=1}^{n-1}}f(x_i)\\=16f({{\sum}_{i=1}^{n-1}}x_i){\oplus}2{{\sum}_{i=1}^{n-1}}(f(x_i+x_n){\oplus}f(x_i-x_n)).$$ We first prove that the solution of the n-dimensional cubic set-valued functional equation is actually the cubic set-valued mapping in [6]. We prove the Hyers-Ulam stability for the set-valued functional equation.

• The Pure and Applied Mathematics
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• v.26 no.4
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• pp.247-254
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• 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.

• 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.

• The Pure and Applied Mathematics
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• v.15 no.2
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• pp.103-110
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• 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.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.3
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• pp.295-307
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• 2019

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

• The Pure and Applied Mathematics
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• v.19 no.4
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• pp.397-407
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• 2012

Let X and Y be vector spaces. We introduce a new type of a cubic functional equation $f$ : $X{\rightarrow}Y$. Furthermore, we assume X is a vector space and (Y, N) is a fuzzy Banach space and then investigate a fuzzy version of the generalized Hyers-Ulam stability in fuzzy Banach space by using fixed point method for the cubic functional equation.