• Korean Journal of Mathematics
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• 제26권4호
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• pp.615-628
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• 2018

In this paper, we introduce the pioneering trigintic functional equation. Moreover, we establish the general solution of the trigintic functional equation and prove the Hyers-Ulam sum and product stabilities of the same equation in multi-Banach spaces by employing the fixed point approach.

• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.957-988
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• 2023

We define new classes of expansive-type mappings in the setting of modular 𝜔^G-metric spaces and prove the existence of common unique fixed point for these classes of expansive-type mappings on 𝜔^G-complete modular 𝜔^G-metric spaces. The results established in this paper extend, improve, generalize and compliment many existing results in literature. We produce some examples to validate our results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제27권1호
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• pp.25-33
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• 2020

In this paper, we consider the following quadratic (ρ₁, ρ₂)-functional equation (0, 1) $$N(2f({\frac{x+y}{2}})+2f({\frac{x-y}{2}})-f(x)-f(y)-{\rho}_1(f(x+y)+f(x-y)-2f(x)-2f(y))-{\rho}_2(4f({\frac{x+y}{2}})+f(x-y)-f(x)-f(y)),t){\geq}{\frac{t}{t+{\varphi}(x,y)}}$$, where ρ₂ are fixed nonzero real numbers with ρ₂ ≠ 1 and 2ρ₁ + 2ρ₂≠ 1, in fuzzy normed spaces. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (ρ₁, ρ₂)-functional equation (0.1) in fuzzy Banach spaces.

• Kyungpook Mathematical Journal
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• 제49권2호
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• pp.289-297
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• 2009

We establish a new method to prove Hyers-Ulam-Rassias stability of the quartic functional equation f(2x + y) + f(2x - y) + 6f(y) = 4[f(x + y) + f(x - y) + 6f(x)] in non-Archimedean normed linear spaces.

• Kyungpook Mathematical Journal
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• 제50권2호
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• pp.315-327
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• 2010

We give a xed point approach to the generalized Hyers-Ulam stability of the cubic equation f(2x + y) + f(2x - y) = 2f(x + y) + 2f(x - y) + 12f(x) in non-Archimedean normed spaces. We will give an example to show that some known results in the stability of cubic functional equations in real normed spaces fail in non-Archimedean normed spaces. Finally, some applications of our results in non-Archimedean normed spaces over p-adic numbers will be exhibited.

• Kyungpook Mathematical Journal
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• 제48권1호
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• pp.45-61
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• 2008

We investigate the generalized Hyers-Ulam-Rassias stability in p-Banach spaces for the following functional equation which is two types, that is, either cubic or quadratic: 2f(x+3y) + 6f(x-y) + 12f(2y) = 2f(x - 3y) + 6f(x + y) + 3f(4y). The concept of Hyers-Ulam-Rassias stability originated essentially with the Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300.

• 충청수학회지
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• 제26권4호
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• pp.907-913
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• 2013

In this paper, we prove the generalized Hyers-Ulam stability of the additive functional inequality $${\parallel}f(2x_1)+f(2x_2)+{\cdots}+f(2x_n){\parallel}{\leq}{\parallel}tf(x_1+x_2+{\cdots}+x_n){\parallel}$$ in Banach spaces where a positive integer $n{\geq}3$ and a real number t such that 2${\leq}$t

• 충청수학회지
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• 제28권3호
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• pp.353-363
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• 2015

In this paper, we investigate the functional equation f(3x+y)+f(3x-y) = f(x+2y)+2f(x-y)+6f(2x)+3f(x)-6f(y) and prove the generalized Hyers-Ulam stability for it in non-Archimedean normed spaces.

• East Asian mathematical journal
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• 제34권5호
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• pp.693-702
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• 2018

In this paper, we consider the generalized Hyers-Ulam stability for the following additive-quadratic functional equation with involution $f(x+2y)-f(2x+y)+f(x+y)+f({\sigma}(x)+y)+f(x)-4f(y)-f({\sigma}(y))=0$ in non-Archimedean spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권1호
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• pp.59-71
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• 2012

In this paper, we prove the stability in random normed spaces via fixed point method for the functional equation $$f(x+y+z)-f(x+y)-f(y+z)-f(x+z)+f(x)+f(y)+f(z)=0$$. by using a fixed point theorem in the sense of L. C$\breve{a}$dariu and V. Radu.