• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.801-812
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• 2023

In this paper, we investigate the superstability for the p-power-radical sine functional equation $$f\(\sqrt[p]{\frac{x^p+y^p}{2}}\)^2-f\(\sqrt[p]{\frac{x^p-y^p}{2}}\)^2=f(x)f(y)$$ from an approximation of the p-power-radical functional equation: $$f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}g(x)h(y),$$ where p is an odd positive integer and f, g, h are complex valued functions. Furthermore, the obtained results are extended to Banach algebras.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.765-774
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• 2021

In this paper, we solve and investigate the superstability of the p-radical functional equations $$f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}f(x)g(y),\\f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}g(x)f(y),$$ which is related to the trigonometric(Kim's type) functional equations, where p is an odd positive integer and f is a complex valued function. Furthermore, the results are extended to Banach algebras.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.4
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• pp.315-327
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• 2022

In this paper, we investigate the transferred superstability for the p-radical sine functional equation $$f\(\sqrt[p]{\frac{x^p+y^p}{2}}\)^2-f\(\sqrt[p]{\frac{x^p-y^p}{2}}\)^2=f(x)f(y)$$ from the p-radical functional equations: $$f({\sqrt[p]{x^p+y^p}})+f({\sqrt[p]{x^p-y^p}})={\lambda}g(x)g(y),\;\\f({\sqrt[p]{x^p+y^p}})+f({\sqrt[p]{x^p-y^p}})={\lambda}g(x)h(y),$$ where p is an odd positive integer, λ is a positive real number, and f is a complex valued function. Furthermore, the results are extended to Banach algebras. Therefore, the obtained result will be forced to the pre-results(p=1) for this type's equations, and will serve as a sample to apply it to the extension of the other known equations.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.387-398
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• 2021

In this paper, we will find solutions and investigate the superstability bounded by constant for the p-radical functional equations as follows: $f\(\sqrt[p]{\frac{x^p+y^p}{2}}\)^2-f\(\sqrt[p]{\frac{x^p-y^p}{2}}\)^2=\;\{(i)\;f(x)f(y),\\(ii)\;g(x)f(y),\\(iii)\;f(x)g(y),\\(iv)\;g(x)g(y).$ with respect to the sine functional equation, where p is an odd positive integer and f is a complex valued function. Furthermore, the results are extended to Banach algebra.

• Journal of the Korean Society of Food Science and Nutrition
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• v.42 no.5
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• pp.721-729
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• 2013

To improve the quality and functionality of the low salt squid Jeot-gal, extracts from three types of medicinal and edible plants (bay leaf, green tea, pine needle) were added. The quality characteristics, bioactivities, and shelf-lives of these preparations were determined at three different fermentation temperatures. The pH decreased more rapidly at higher temperatures, while the amount of volatile basic nitrogen (VBN), total viable cells, and amino nitrogen ($NH_2$-N) increased. The shelf-lives of Jeot-gal with natural plant extracts at $10^{\circ}C$ were 34~35 days, similar to the control. The major free and compositional amino acids of Jeot-gal were glutamic acid, proline, and alanine, while the major nucleotides (and related compounds) were hypoxanthine and inosine. In bioactivity assays, samples supplemented with plant extracts showed higher bioactivities than the control. The DPPH radical scavenging activity of ethanol extracts from Jeot-gal were stronger than the water extracts; in contrast, the water extracts were stronger for hydrogen peroxide scavenging activity. However, superoxide dismutase (SOD)-like activity and ${\beta}$-glucuronidase inhibitory activity were moderately low at 20 mg/mL. Based on sensory evaluation results, the quality of low salt squid Jeot-gal with natural plant extracts is similar to the control. Therefore, low salt squid Jeot-gal with natural plant extracts can be commercialized as a functional fermented food.