• 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.

• 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.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.343-359
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• 2021

The aim of this paper is to obtain the general solution of the 2-variable radical functional equations $f({\sqrt[k]{x^k+z^k}},\;{\sqrt[{\ell}]{y^{\ell}+w^{\ell}}})=f(x,y)+f(z,w)$, x, y, z, w ∈ ℝ, for f a mapping from the set of all real numbers ℝ into a vector space, where k and ℓ are fixed positive integers. Also using the fixed point result of Brzdęk and Ciepliński [11, Theorem 1] in (2, 𝛽)-Banach spaces, we prove the generalized hyperstability results of the 2-variable radical functional equations. In the end of this paper we derive some consequences from our main results.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1511-1525
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• 2014

In this paper, we prove the generalized Hyers-Ulam stability results controlled by considering approximately mappings satisfying conditions much weaker than Hyers and Rassias conditions for radical quadratic and radical quartic functional equations in quasi-${\beta}$-normed spaces.

• 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.

• Korean Journal of Medicinal Crop Science
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• v.24 no.4
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• pp.263-270
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• 2016

Background: In this study, microwave extraction was used, which is an effective method to extract useful bioactive substances as it requires low quantities of solvent and short time periods. The aim of this study was to determine the optimal extraction conditions for Agrimonia pilosa Ledeb. Methods and Results: The independent variables were ethanol concentration, microwave power, and extraction time, each of which had five levels. The dependent variables were total polyphenol and total flavonoid content, and DPPH radical scavenging activity. To determine the optimal extraction conditions for bioactive compounds, a response surface methodology was employed. Contour maps were generated from polynomial equations. The optimal conditions were then assumed by superimposing these contour maps. Based on the resulting graph, the optimal microwave extraction conditions for Agrimonia pilosa Ledeb were determined as 42 - 48% ethanol concentration, 240 - 280W microwave power, and 13 - 20 min of extraction time. Conclusions: Ethanol concentration had a significant effect on microwave extraction, in terms of total polyphenol and total flavonoid content, as well as DPPH radical scavenging activity. Microwave power and extraction time influenced the total polyphenol content, but not the total flavonoid content or the DPPH radical scavenging activity.

• Korean Journal of Food Science and Technology
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• v.37 no.2
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• pp.233-240
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• 2005

To discover new functional materials using edible plants, antioxidant activities of methanol extracts from various parts of seven wild vegetables were investigated in vitro. Total polyphenol contents, determined by Folin-Denis method, varied from 16.74 to $130.22{\mu}g/mg$. Radical-scavenging activities of methanol extracts were examined using ${\alpha},\;{\alpha}-diphenyl-{\beta}-pirrylhydrazyl$ (DPPH) radicals and 2,2'-azino-bis(3-ethylbenzthiazoline-6-sulfonic acid) (ABTS) assay. Inhibition effects on peroxidation of linoleic acid determined by ferric thiocyanate (FTC) method and on oxidative degradation of 2-deoxy-D-ribose in Fenton-type reaction system were dose-dependent. Athyrium acutipinulum Kodama (leaf and rood), Achyranthes japonica (Miq.) Nakai (seed), and Solidago virga-aurea var. gigantea Nakai (root) showed relatively high antioxidant activities in various systems.

• Journal of Nutrition and Health
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• v.54 no.1
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• pp.116-128
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• 2021

Purpose: The extraction conditions for bioactive components from peanut shells, which is a byproduct of peanut processing, were optimized to enhance the total phenolic content (TPC, Y1), total flavonoid content (TFC, Y2), and 2,2-diphenyl-1-picrylhydrazyl radical scavenging activity (RSA, Y3). In addition, this study evaluated the anti-obesity effect of peanut shell extract. Methods: Optimization of ultrasonic-assisted extraction (UAE) was performed using a response surface methodology. The independent variables applied for extraction were time (X1: 5.0-55.0), temperature (X2: 26.0-94.0), and ethanol concentration (X3: 0.0%-99.5%). Quadratic regression models were derived based on the results of 17 experimental sets, and an analysis of the variance was performed to verify its accuracy and precision of the regression equations. Results: When evaluating the effects of independent variables on responses using statistically-based optimization, the independent variable with the most significant effect on the TPC, TFC, and RSA was the ethanol concentration (p = 0.0008). The optimal extraction conditions to satisfy all three responses were 35.8 minutes, 82.7℃, and 96.0% ethanol. Under these conditions, the inhibitory activities of α-glucosidase and pancreatic lipase by the extract were 86.4% and 78.5%, respectively. Conclusion: In this study, UAE showed superior extraction efficiency compared to conventional hot-water extraction in the extraction of polyphenols and bioactive materials. In addition, α-glucosidase and pancreatic lipase inhibitory effects were identified, suggesting that peanut shells can be used as effective antioxidants and anti-obesity agents in functional foods and medicines.