• 대한수학회보
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• 제53권4호
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• pp.1157-1169
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• 2016

We find the distributional solutions of the Wilson's functional equations $$u{\circ}T+u{\circ}T^{\sigma}-2u{\otimes}v=0,\\u{\circ}T+u{\circ}T^{\sigma}-2v{\otimes}u=0,$$ where $u,v{\in}{\mathcal{D}}^{\prime}({\mathbb{R}}^n)$, the space of Schwartz distributions, T(x, y) = x + y, $T^{\sigma}(x,y)=x+{\sigma}y$, $x,y{\in}{\mathbb{R}}^n$, ${\sigma}$ an involution, and ${\circ}$, ${\otimes}$ are pullback and tensor product of distributions, respectively. As a consequence, we solve the $Erd{\ddot{o}}s$' problem for the Wilson's functional equations in the class of locally integrable functions. We also consider the Ulam-Hyers stability of the classical Wilson's functional equations $$f(x+y)+f(x+{\sigma}y)=2f(x)g(y),\\f(x+y)+f(x+{\sigma}y)=2g(x)f(y)$$ in the class of Lebesgue measurable functions.

• 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.

• 대한수학회논문집
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• 제35권3호
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• pp.711-722
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• 2020

Given a semigroup S generated by its squares equipped with an involutive automorphism 𝝈 and a multiplicative function 𝜇 : S → ℂ such that 𝜇(x𝜎(x)) = 1 for all x ∈ S, we determine the complex-valued solutions of the following functional equations f(xy) + 𝜇(y)f(𝜎(y)x) = 2f(x)g(y), x, y ∈ S and f(xy) + 𝜇(y)f(𝜎(y)x) = 2f(y)g(x), x, y ∈ S.

• 대한수학회논문집
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• 제38권4호
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• pp.1063-1074
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• 2023

Let S be a semigroup. We determine the complex-valued solutions of the following functional equation f(xy) + 𝜇(y)f(𝜎(y)x) = 2f(x)g(y), x, y ∈ S, where 𝜎 : S → S is an automorphism, and 𝜇 : S → ℂ is a multiplicative function such that 𝜇(x𝜎(x)) = 1 for all x ∈ S.

• Korean Journal of Mathematics
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• 제29권4호
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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.

• Korean Journal of Mathematics
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• 제16권1호
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• pp.103-114
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• 2008

In this paper, we investigate the superstability problem for the pexiderized cosine functional equations f(x+y) +f(x−y) = 2g(x)h(y), f(x + y) + g(x − y) = 2f(x)g(y), f(x + y) + g(x − y) = 2g(x)f(y). Consequently, we have generalized the results of stability for the cosine($d^{\prime}Alembert$) and the Wilson functional equations by J. Baker, $P.\;G{\check{a}}vruta$, R. Badora and R. Ger, and G.H. Kim.

• 충청수학회지
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• 제35권4호
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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.

• 대한간호학회지
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• 제44권1호
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• pp.75-85
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• 2014

Purpose: The aim of this study was to explore how individual factors, physiologic factors, symptoms, environmental factors, functional status and health perception predict the quality of life (QOL) for older adults with osteoarthritis and to provide guidelines for interventions and strategies to improve QOL in these patients. The conceptual model was based on the Wilson and Cleary's Model. Methods: Data were analyzed using SPSS WIN 20.0 and AMOS 19.0 program. Results: The proposed model was a good fit for the data based on the model fit indices. Based on the constructed model, individual factors, social support, functional status and health perception were founded to have direct effects on QOL. Symptom had a indirect effect on QOL. Social support had a significant effect on QOL, and this model explained 63.6% of the variance in QOL. Conclusion: The results of this study suggest that nursing strategies to increase QOL in this population should contain social support to promote QOL and manage functional limitations and health perception.

• 대한간호학회지
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• 제50권4호
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• pp.554-570
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• 2020

Purpose: This study aimed to develop and test a structural equation model of health-related quality of life among older women following bilateral total knee replacement based on a literature review and Wilson and Cleary's model of health-related quality of life. Methods: One hundred ninety three women who were diagnosed with osteoarthritis, were older than 65 years, and were between 13 weeks and 12 months of having a bilateral total knee replacement were recruited from an outpatient clinic. Data were collected from July 2017 to April 2018 using a structured questionnaire and medical records. Data were analyzed using SPSS/WIN 22.0, AMOS 22.0, and Smart PLS 3.2.4. Results: The fitness of the hypothetical model was good, with coefficients of determination (R²) ranging between .28 and .75 and predictive relevance (Q²) between .26 and .73. The standardized root mean square residual of the model fit indices for the hypothetical model was .04; which explained 64.2% of physical and 62.5% of mental health-related quality of life. Self-efficacy, symptom status, functional status, and general health perceptions had a significant direct effect on physical health-related quality of life, while social support, symptom status, and general health perceptions had a significant direct effect on participants' mental-health-related quality of life. Conclusion: To improve the physical and mental quality of life of older women who receive bilateral knee replacement, nursing-based intervention strategies that reduce symptoms, improve functional status, and increase health perceptions, self-efficacy, and social support are needed. The most important factor is the symptom status.