• 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.36 no.2
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• pp.107-123
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• 2023

In this paper, we present some hyperstability results for a general quintic functional equation and a general septic functional equation.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.295-306
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• 2021

The general sextic functional equation is a generalization of many functional equations such as the additive functional equation, the quadratic functional equation, the cubic functional equation, the quartic functional equation and the quintic functional equation. In this paper, motivating the method of Găvruta [J. Math. Anal. Appl., 184 (1994), 431-436], we will investigate the stability of the general sextic functional equation.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.447-456
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• 2004

In this paper we investigate the Hyers-Ulam-Rassias stability of a 4-dimensional quadratic functional equation (equation omitted).

• Journal of the Chungcheong Mathematical Society
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• v.14 no.1
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• pp.73-83
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• 2001

In this paper, we solve a Jensen type functional equation and prove the stability of the Jensen type functional equation.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.389-399
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• 2002

In this paper we solve a quadratic Jensen type functional equation (equation omitted) and prove the stability of this equation.

• 보존과학연구
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• s.31
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• pp.79-88
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• 2010

Paper cultural heritages experience chemical and physical deterioration due to various factors including preservation environments and the property of paper materials1). Thus, it is important to develop optimal preservation and restoration methods for the damaged paper cultural heritages. Currently, lining is a popular treatment for the restoration of paper cultural heritages in Korea. Since lining paper is a layer of paper directly attached to the inside of cultural heritages for protection, understanding of the preservation properties of lining paper is primarily needed in order to devise the better preservation methods. The main material of lining paper is the paper mulberry, but additives such as chalk and white clay is sometimes used to enhance the preservation properties of lining paper. To date, the properties of the functional lining paper containing these additives have been not fully understood yet. In this study, dry heating aging at $105^{\circ}C$ and biological aging by the Aspergillus versicolor and Penicillium polonicum for the lining paper, which is made from paper mulberry and the chalk, are carried out to evaluate changes in their preservation properties by these aging factors. As a result, it is found that the functional lining paper containing 25.1% of chalk can control the growth of fungi, while the paper containing 32.7% of chalk do not show any protection effect. However, the functional lining paper added by chalk is more aged than the lining paper made from paper mulberry by dry heating accelerated aging.

• 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.

• Pediatric Gastroenterology, Hepatology & Nutrition
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• v.12 no.sup1
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• pp.103-110
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• 2009

Functional gastrointestinal disorders are among the most common medical problems in children. Abdominal pain-related functional gastrointestinal disorders can be categorized as functional dyspepsia, irritable bowel syndrome, abdominal migraine and childhood functional abdominal pain according to the Rome III criteria for pediatric functional gastrointestinal disorders. The aim of this paper was to examine the evidence supporting the use of the range of therapeutic options available for functional gastrointestinal disorders.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.397-411
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• 2010

In this paper, we will investigate the superstability for the sine functional equation from the following Pexider type functional equation: $f(x+y)-g(x-y)={\lambda}{\cdot}h(x)k(y)$ ${\lambda}$: constant, which can be considered an exponential type functional equation, the mixed functional equation of the trigonometric function, the mixed functional equation of the hyperbolic function, and the Jensen type equation.