• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.673-692
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• 2024

In this work, an alternative fashion of the multi-Jensen is introduced. The structures of the multi-Jensen and the multi-Euler-Lagrange-Jensen mappings are described. In other words, the system of n equations defining each of the mentioned mappings is unified as a single equation. Furthermore, by applying a fixed point theorem, the Hyers-Ulam stability for the multi-Euler-Lagrange-Jensen mappings in the setting of Banach spaces is established. An appropriate counterexample is supplied to invalidate the results in the case of singularity for multiadditive mappings.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.133-142
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• 2008

Given an $m{\in}\mathbb{N}$ and two vector spaces V and W, a function f : $V^m{\rightarrow}W$ is called multi-Jensen if it satisfies Jensen's equation in each variable separately. In this paper we unify these m Jensen equations to obtain a single functional equation for f and prove its stability in the sense of Hyers-Ulam, using the so-called direct method.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.729-737
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• 2008

In this paper we characterize multi-Jensen functions f : $V^n\;{\rightarrow}\;W$, where n is a positive integer, V, W are commutative groups and V is uniquely divisible by 2. Moreover, under the assumption that f : $\mathbb{R}\;{\rightarrow}\;\mathbb{R}$ is Borel measurable, we obtain representation of f (respectively, f, g, h : $\mathbb{R}\;{\rightarrow}\;\mathbb{R}$) such that the Jensen difference $$2f\;\(\frac{x\;+\;y}{2}\)\;-\;f(x)\;-\;f(y)$$ (respectively, the Pexider difference $$2f\;\(\frac{x\;+\;y}{2}\)\;-\;g(x)\;-\;h(y))$$ takes values in a countable subgroup of $\mathbb{R}$.

• The Pure and Applied Mathematics
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• v.18 no.2
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• pp.161-172
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• 2011

In this paper we investigate the Hyers-Ulam stability of a Jensen type functional equation in multi-normed spaces and then extend the result to multi-normed left modules over a normed algebra A.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.513-519
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• 2007

In this paper, we obtain the general solution and the stability of the multi-dimensional Jensen's functional equation $$2f(\frac{x_1+y_1}{2},\;\cdots,\;\frac{x_n+y_n}{2})=f(x_1,\;\cdots,\;x_n)+f(y_1,\;\cdots,\;y_n)$$. The function f given by $f(x_1,\;\cdots,\;x_n)=a_1x_1+{\cdots}+a_nx_n+b$ is a solution of the above functional equation.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.319-333
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• 2013

Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces: $${\sum_{1{\leq}i_<j{\leq}n}}\;f(\frac{r_ix_i+r_jx_j}{k})=\frac{n-1}{k}{\sum_{i=1}^n}r_if(x_i)$$.

• The Korean Journal of Financial Management
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• v.14 no.2
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• pp.21-55
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• 1997

본 연구는 기업규모, 장부가치/시장가치 비율, 순이익/주가 비율, 현금흐름/주가 비율, 레버리지 등 기본적 변수를 사용하여 주식수익률에 유의적인 변수를 확인하고, 또한 Fama and French(1993) 등에 의해서 제시된 다요인모형(multi-factor model)이 한국주식시장에서 적용가능한 지를 살펴보았다. 이를 위하여 본 연구에서는 Fama and MacBeth(1973)의 횡단면회귀모형과 Black, Jensen, and Scholes (1972)의 시계열모형을 사용하였으며, 실증분석결과를 요약하면 다음과 같다. 먼저 횡단면분석결과에 의하면, 장부가치/시장가치 비율(BE/ME), 현금흐름/주가 비율(C/P) 등이 주식수익률의 횡단면적 차이를 설명할 수 있는 유의적인 변수로 나타났다. 그리고 통계적 의미에서는 1월효과가 존재한다고 보기 어려우나, 경제적 의미에서 1월효과가 존재하는 것으로 생각된다. 시계열분석결과에 의하면, 시장요인, 기업규모요인, 장부가치/시장가치요인(또는 현금흐름/주가요인) 등의 3요인에 의해서 국내 주식수익률의 공통적 변동을 잘 설명할 수 있다. 즉 국내 증권시장에서도 Fama and French(1993)의 3요인모형이 성립될 수 있는 것으로 판단된다.

• Tuberculosis and Respiratory Diseases
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• v.59 no.3
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• pp.250-256
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• 2005

Background : Fluoroquinolone drugs are an important anti-tuberculous agent for the treatment of multi-drug resistant tuberculosis. However, many drugs belonging to the fluoroquinolones have different cross resistance to each other. Methods : Sixty-three ofloxacin (OFX) resistant and 10 pan-susceptible M. tuberculosis isolates were selected, and compared for their cross resistance using a proportion method on Lowenstein-Jensen media, containing ofloxacin (OFX), ciprofloxacin (CIP), levofloxacin (LVX), moxifloxacin (MXF), gatifloxacin (GAT) and sparfloxacin (SPX), at concentrations ranging from 0.5 to $3{\mu}g/ml$. DNA extracted from the isolates was directly sequenced after amplifying from the gyrA and gyrB genes. Results : The 63 OFX resistant M. tuberculosis isolates showed complete cross resistance to CIP, but only 90.5, 44.4, 36.5 and 46.0% to LVX, MXF, GAT, and to SPX, respectively. Fifty-one of the isolates (81.0%) had point mutations in codons 88, 90, 91 and 94 in gyrA, which are known to be correlated with OFX resistance. The Gly88Ala, Ala90Valand Asp94Ala mutations in gyrA showed a tendency to be susceptible to MXF, GAT and SPX. Only 4 isolates had mutations in the gyrB gene, which did not affect the OFX resistance. Conclusion : About 60% of the OFX resistant M. tuberculosis isolates were susceptible to GAT, SPX and MXF. These fluoroquinolones may be useful in the treatment of TB patients showing OFX resistance.

• Tuberculosis and Respiratory Diseases
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• v.59 no.3
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• pp.257-265
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• 2005

Background : Rifabutin (ansamycin) is a spiro-piperidyl rifamycin, which is highly active against Mycobacterium tuberculosis. It has been found that some clinical isolates of tubercle bacilli that are resistant to rifampicin are susceptible to rifabutin, with some patients with multi-drug resistant pulmonary tuberculosis having shown favorable clinical and bacteriological responses to the rifabutin. This study was conducted to find the proportion of rifabutin-susceptible strains among rifampicin-resistant isolates from Korean MDR-TB patients, and investigate the presence of specific rpoB mutations, which may confer resistance to rifampicin, but not to rifabutin. Methods : 201 rifampicin-resistant and 50 pan-susceptible M. tuberculosis isolates were randomly selected for this study. The isolates were retested at rifampicin and rifabutin concentrations of 0, 20, 40 and $80{\mu}g/ml$, respectively. The isolates that grew at and/or over a rifabutin concentration of $20{\mu}g/ml$ were judged rifabutin-resistant. The rpoB gene was extracted from the isolates, and then amplified for direct sequencing to investigate specific rpoB mutations that conferred rifabutin- susceptibility but rifampicin-resistance. Results : Out of the 201 rifampicin-resistant M. tuberculosis, 41 strains (20.4%) were susceptible to rifabutin using the absolute concentration method on Lowenstein-Jensen media. The rpoB mutation types that showed susceptibility to rifabutin were Leu511Pro, Ser512Arg, Gln513Glu, Asp516Ala, Asp516Gly, Asp516Val, Asp516Tyr, Ser522Leu, His526Asn, His526Leu, His526Cys, Arg529Pro and Leu533Pro. A reverse hybridization technique was able to detect 92.5% of the rifabutin-susceptible isolates, with a specificity of 96.1% among 195 M. tuberculosis isolates with the rpoB mutation. Conclusions : Around 20% of the rifampicin-resistant isolates in Korea showed susceptibility to rifabutin, which was associated with some specific mutations of rpoB. Rifabutin could be used for the treatment of MDR-TB patients, especially when drug susceptibility testing reveals susceptibility to rifabutin.