• 대한수학회보
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• 제56권3호
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• pp.779-787
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• 2019

In this paper, we study two functional equations with two unknown functions from an Abelian group into a commutative ring without zero divisors. The two equations are generalizations of Swiatak's functional equations with an involution. We determine the general solutions of the two functional equations and the properties of the general solutions of the two functional equations under three different hypotheses, respectively. For one of the functional equations, we establish the Hyers-Ulam stability in the case that the unknown functions are complex valued.

• 충청수학회지
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• 제26권2호
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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.

• Korean Journal of Mathematics
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• 제16권3호
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• pp.369-378
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• 2008

The aim of this paper is to study the stability problem for the pexider type trigonometric functional equation f(x + y) − f(x−y) = 2g(x)h(y), which is related to the d'Alembert, the Wilson, the sine, and the mixed trigonometric functional equations.

• 대한수학회보
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• 제46권1호
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• pp.11-23
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• 2009

In this paper, we prove the generalized Hyers-Ulam stability of the functional inequalities associated with additive functional mappings. Also, we find the solution of these inequalities which satisfy certain conditions.

• 펄프종이기술
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• 제39권3호
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• pp.60-69
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• 2007

This study developed rice packaging paper with exterminating performance against rice weevils such as Tenebroides mauritanicus and Sitophilus oryzae. The exterminating performance of packaging paper was given by treatment of garlic extractives and pine-leaf powder, respectively. For the exterminating test, rice weevils were put in petri dish containing non-treated packaging paper and functional packaging paper for twenty days. Right after being put in the petri dish, the rice weevils moved fast toward the area in the non-treated paper escaping from that in the functional paper. The lethality of the rice weevils on the functional paper reached over 50 per cent. The physical properties of the functional packaging paper were rarely changed in spite of treatment of the exterminating agents.

• 충청수학회지
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• 제20권2호
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• pp.173-182
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• 2007

In this paper, we prove the Cauchy-Rassias stability of derivations on quasi-Banach algebras associated to the Cauchy functional equation and the Jensen functional equation. We use the Cauchy-Rassias inequality that was first introduced by Th. M. Rassias in the paper "On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300".

• Journal of applied mathematics & informatics
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• 제41권3호
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• pp.469-485
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• 2023

In this paper, we investigate the Hyers-Ulam-Rassias stability for a Drygas functional equation g(u + v) + g(u - v) = 2g(u) + g(v) + g(-v) in the setting of quasi-Banach space using fixed point approach. Also, we give general results on hyperstability of a Drygas functional equation. The results obtain in this paper extend various previously known results in the setting of quasi-Banach space. Some examples are also illustrated.

• 한국포장학회지
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• 제22권3호
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• pp.49-58
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• 2016

Corrugated board provides packaging for most diverse industries with a share of over 50%, due to the numerous advantages they offer a good protection of the products. In other hand corrugated board fails in environmental conditions, indicating that relative humidity or temperature is higher. These effects directly damage the product packaged. To overcome on this problem recently corrugated boards produced with functional material, "functional corrugated boards," have become more available in the current market. A number of commercialized forms of functional material are coated or composited products with inorganic materials, for example "Nano clay" as representative. However, although the use of functional materials is increasing in corrugated boards, the several concerns such as over cost, environmental friendly materials, recycling, and toxicity affect consumer perceptions and acceptance. In the past, number of researcher focused on process of box compression and the utility of box compression testing etc., best of our knowledge there is no review paper which focus on the functional corrugated boards used in food packaging applications. This paper aims to review the availability of functional corrugated boards in the current market, past research studies on functional material and present the current status of functional corrugated boards in leading countries.

• 펄프종이기술
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• 제45권3호
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• pp.9-19
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• 2013

This research was performed to make functional papers by using the waste of herbal medicine such as Astragalus membranaceus, Angelica acutiloba, and Artemisia capillaris as additives, and to evaluate their physical and optical properties of the manufactured paper. The physical and optical properties were decreased with the increase of the amount of herbal medicine. Of those manufactured papers, the functional paper with Artemisia capillaris showed the dramatic decrease in its physical properties. Adding the herbal medicine waste as additives developed the aesthetic pattern on the surface of the manufactured paper. The paper showing the black pattern on white surface was most favored. Different patterns could be made by changing the size of fibers and the amount of wastes. There was odor emitted from the paper due to the herbal medicine waste, which make the paper to have a potential for the diverse purpose. The herbal medicine waste can be applied to replace weighting agents in the manufacturing process of paper or used for the fuctional additives, resulting in the reduce of the quantity of a pulp consumed. The paper with 10-20% Angelica acutiloba waste were thought to have the most excellent quality on the process point of view.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.363-372
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• 2010

In this paper we obtain the Hyers-Ulam stability of functional equations $f(x+y)=f(x)+f(y)+In\;{\alpha}^{2xy-1}$ and $f(x+y)=f(x)+f(y)+In\;{\beta(x,y)^{-1}$ which is related to the exponential and beta functions.