• Kyungpook Mathematical Journal
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• 제60권1호
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• pp.133-144
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• 2020

We will prove the generalized Hyers-Ulam stability of cubic-quadratic-additive type functional equations and general cubic functional equations whose solutions are cubic-quadratic-additive mappings and general cubic mappings, respectively.

• Korean Journal of Mathematics
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• 제19권4호
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• pp.437-451
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• 2011

In this paper, we prove the stability in random normed spaces via fixed point method for the functional equation $$f(x+2y)-2f(x+y)+2f(x-y)-f(x-2y)=0$$.

• 대한수학회보
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• 제42권1호
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• pp.133-148
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• 2005

In this paper, we obtain the general solution of a gen-eralized quadratic and additive type functional equation f(x + ay) + af(x - y) = f(x - ay) + af(x + y) for any integer a with a $\neq$ -1. 0, 1 in the class of functions between real vector spaces and investigate the generalized Hyers- Ulam stability problem for the equation.

• Kyungpook Mathematical Journal
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• 제53권2호
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• pp.219-232
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• 2013

In this paper, we investigate the stability of the functional equation $$f(x+2y)-2f(x+y)+2f(x-y)-f(x-2y)=0$$ by using the fixed point theory in the sense of L. C$\breve{a}$dariu and V. Radu.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.563-572
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• 2005

In this paper, we obtain the general solution and the generalized Hyers-Ulam stability of the additive-quadratic functional equation f(x + y, z + w) + f(x + y, z - w) = 2f(x, z)+2f(x, w)+2f(y, z)+2f(y, w).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권1호
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• pp.65-80
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• 2010

In [17, 18], the fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations in fuzzy Banach spaces: (0.1) f(x + y) + f(x - y) = 2f(x) + 2f(y), (0.2) f(ax + by) + f(ax - by) = $2a^2 f(x)\;+\;2b^2f(y)$ for nonzero real numbers a, b with $a\;{\neq}\;{\pm}1$.

• 충청수학회지
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• 제28권2호
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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.

• East Asian mathematical journal
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• 제31권5호
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• pp.627-634
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• 2015

In this paper, we investigate the following orthogonally additive-quadratic functional equation f(2x + y) - f(x + 2y) - f(x + y) - f(y - x) - f(x) + f(y) + f(2y) = 0. and prove the generalized Hyers-Ulam stability for it in orthogonality spaces by using the fixed point method.

• Kyungpook Mathematical Journal
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• 제58권2호
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• pp.291-305
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• 2018

In this paper, we prove a general uniqueness theorem which is useful for proving the uniqueness of the relevant additive mapping, quadratic mapping, cubic mapping, quartic mapping, or the additive-quadratic-cubic-quartic mapping when we investigate the (generalized) Hyers-Ulam stability.

• 충청수학회지
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• 제30권2호
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• pp.239-249
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• 2017

In this paper, we approximate a fuzzy almost cubic function by a cubic function in a fuzzy sense. Indeed, we investigate solutions of the following cubic functional equation $$3f(kx+y)+3f(kx-y)-kf(x+2y)-2kf(x-y)-3k(2k^2-1)f(x)+6kf(y)=0$$. and prove the generalized Hyers-Ulam stability for it in fuzzy Banach spaces.