• 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.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.269-275
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• 2021

Let ℝ be the set of real numbers, f, g : ℝ → ℝ and �� ≥ 0. In this paper, we consider the stability of partially pexiderized exponential-radical functional equation $$f({\sqrt[n]{x^N+y^N}})=f(x)g(y)$$ for all x, y ∈ ℝ, i.e., we investigate the functional inequality $$\|f({\sqrt[n]{x^N+y^N}})-f(x)g(y)\|{\leq}{\epsilon}$$ for all x, y ∈ ℝ.

• 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.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.149-161
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• 2010

We adopt the idea of $C{\breve{a}}dariu$ and Radu to prove the generalized Hyers-Ulam stability of generalized Jordan triple derivation in Banach algebra. In addition, we take account of problems for generalized Jordan triple linear derivation in Banach algebra.

• Applied Chemistry for Engineering
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• v.3 no.4
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• pp.678-685
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• 1992

The effects of functional monomers on the pressure sensitive adhesive proporties were studied. Acrylic acid and other monomers were copolymerized by radical solution polymerization and their properties were measured. The desirability function methodology was applied to obtain optimum pressure sensitive adhesive properties. Acrylic acid showed more effective than acrylamide on peel strength increase. On the other hand acrylamide showed more effective than acrylic acid on tack decrease. The optimum monomer ratio of the acrylic pressure sensitive adhesive recipe containing n-butylacrylate 81.7 mole%, acrylic acid 8.0 mole%, acrylamide 2.1 mole% and vinylacetate 8.2 mole% was obtained to result from the statistical analysis with the desirability function methodology. The estimated regression equation of desirability function(D) is as follows: $D=.857+.072X_1-.114X_2-.027X_3-.126X_1{^2}-.046X_1{\cdot}X_2-.063X_1{\cdot}X_3-.152X_2{^2}+.027X2{\cdot}X_3-.120X_3{^2}$ $X_1$:coded acylic acid, $X_2$:coded acylamide, $X_3$:coded vinylacetate

• 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.