• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.295-306
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• 2024

In this work, we investigate the generalized Hyers-Ulam stability of quadratic functional inequality in modular spaces satisfying ∆₂-conditions and Fatou property, and in 𝛽-homogeneous Banach spaces.

• Journal of the Architectural Institute of Korea Structure & Construction
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• v.35 no.1
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• pp.37-46
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• 2019

In order to present the enhancement direction for the military administrative facilities, that can satisfy the user demands and achieve cost-effectiveness the goal of public projects, this research analyzes the features of functional spaces using Analytical Hierarchy Process(AHP). Basically, the scope is selected to four facilities commander office, private office, public office, and meeting room, because they have an effect on military administrative facilities. Since the space is established by a combination of their own functions, this research begins with an analysis of functional spaces of military administrative facilities, which is verified through literature review and interview with expert. Thereafter, an AHP survey is conducted to military personnel to analyze the priority of functional spaces and to re-classify the functional spaces of each Military administrative facilities. Resultingly, the difference of functional spaces preference according to ranks and facility type are identified. Even though the same military facilities, it means that user satisfaction is different. Therefore, user satisfaction should be considered for each facility at the construction plan. It can minimize overlapped and unused spaces, which can help ensure cost-effectiveness. Consequently, this research suggested the methodology and the process that can take user satisfaction and can support the enhancement of military facilities standards.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.287-296
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• 2013

In this paper, we investigate additive functional inequalities in paranormed spaces. Furthermore, we prove the Hyers-Ulam stability of additive functional inequalities in paranormed spaces.

• Kyungpook Mathematical Journal
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• v.53 no.3
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• pp.419-433
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• 2013

In this paper, we prove the generalized Hyers-Ulam-Rassias stability for a system of functional equations, called general system of nonlinear functional equations, in non-Archimedean normed spaces and Menger probabilistic non-Archimedean normed spaces.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.393-399
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• 2015

W. Park [J. Math. Anal. Appl. 376 (2011) 193-202] proved the Hyers-Ulam stability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces. But there are serious problems in the control functions given in all theorems of the paper. In this paper, we correct the statements of these results and prove the corrected theorems. Moreover, we prove the superstability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces under the original given conditions.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.2
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• pp.199-230
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• 2018

In this paper, we introduce the general form of a viginti functional equation. Then, we find the general solution and study the generalized Ulam-Hyers stability of such functional equation in multi-Banach spaces by using fixed point technique. Also, we indicate an example for non-stability case regarding to this new functional equation.

• 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.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.401-411
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• 2014

In this paper, we prove the generalized Hyers-Ulam stability of the following Jensen type functional equation $$f(\frac{x-y}{n}+z)+f(\frac{y-z}{n}+x)+f(\frac{z-x}{n}+y)=f(x)+f(y)+f(z)$$ in p-Banach spaces for any fixed nonzero integer n.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.373-388
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• 2010

We introduce mixed cubic-quartic functional equations. And using the fixed point method, we prove the generalized Hyers-Ulam stability of cubic-quartic functional equations on random normed spaces.

• The Pure and Applied Mathematics
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• v.23 no.3
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• pp.265-285
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• 2016

In this paper, we introduce functional equations in G-normed spaces and we prove the Hyers-Ulam stability of an additive-quadratic-cubic-quartic functional equation in complete G-normed spaces by using the fixed point method.