• Title, Summary, Keyword: Wilson's functional equation

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DISTRIBUTIONAL SOLUTIONS OF WILSON'S FUNCTIONAL EQUATIONS WITH INVOLUTION AND THEIR ERDÖS' PROBLEM

  • Chung, Jaeyoung
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.4
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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.

VARIANTS OF WILSON'S FUNCTIONAL EQUATION ON SEMIGROUPS

  • Ajebbar, Omar;Elqorachi, Elhoucien
    • Communications of the Korean Mathematical Society
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    • v.35 no.3
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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 �� and a multiplicative function �� : S → ℂ such that ��(x��(x)) = 1 for all x ∈ S, we determine the complex-valued solutions of the following functional equations f(xy) + ��(y)f(��(y)x) = 2f(x)g(y), x, y ∈ S and f(xy) + ��(y)f(��(y)x) = 2f(y)g(x), x, y ∈ S.

Structural Equation Modeling on Quality of Life in Older Adults with Osteoarthritis (퇴행성 관절염 노인의 삶의 질 구조모형)

  • Oh, Jihyun;Yi, Myungsun
    • Journal of Korean Academy of Nursing
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    • v.44 no.1
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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.

A Structural Equation Model of Health-Related Quality of Life among Older Women Following Bilateral Total Knee Replacement (양측 슬관절 전치환술 여성노인의 건강관련 삶의 질 구조모형)

  • Lee, Hyun Ok;Yoo, Jae Soon
    • Journal of Korean Academy of Nursing
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    • v.50 no.4
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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.