• Kyungpook Mathematical Journal
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• 제46권2호
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• pp.211-217
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• 2006

In this paper, we have shown that the convergence of one-step, two-step and three-step iterations is equivalent, which are known as Mann, Ishikawa and Noor iteration procedures, for a special class of Lipschitzian operators defined in a closed, convex subset of an arbitrary Banach space.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.753-762
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• 2010

Let K be a nonempty closed convex subset of a real Hilbert space H. Let T : K $\rightarrow$ K be a nonexpansive mapping with a nonempty fixed point set Fix(T). Let f : K $\rightarrow$ K be a contraction mapping. Let {$\alpha_n$} and {$\beta_n$} be sequences in (0, 1) such that $\lim_{x{\rightarrow}0}{\alpha}_n=0$, (0.1) $\sum_{n=0}^{\infty}\;{\alpha}_n=+{\infty}$, (0.2) 0 < a ${\leq}\;{\beta}_n\;{\leq}$ b < 1 for all $n\;{\geq}\;0$. (0.3) Then it is proved that the modified Krasnoselski-Mann iterative sequence {$x_n$} given by {$x_0\;{\in}\;K$, $y_n\;=\;{\alpha}_{n}f(x_n)+(1-\alpha_n)x_n$, $n\;{\geq}\;0$, $x_{n+1}=(1-{\beta}_n)y_n+{\beta}_nTy_n$, $n\;{\geq}\;0$, (0.4) converges strongly to a point p $\in$ Fix(T} which satisfies the variational inequality

$\leq$ 0, z $\in$ Fix(T). (0.5) This result improves and extends the corresponding results of Yao et al[Y.Yao, H. Zhou, Y. C. Liou, Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings, J Appl Math Com-put (2009)29:383-389.

• 한국농공학회논문집
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• 제57권6호
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• pp.153-162
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• 2015

In this study, we analyzed the trends of water quality along the main stream in Nakdong river basin using the recent data and seasonal Mann-Kendall test. Monthly averaged values of DO, BOD, SS, COD, TN, and TP from 1989 to 2014 for 14 stations (including 2 TMDLs stations) were used in the study. The trend analysis results showed that BOD and TP at most stations has decreasing temporal trend except a few stations while COD and SS showed increasing trend at most stations. Temporal trends in TN at 8 stations were found to be statistically significant and 5 of them showed increasing temporal trend. Temporally averaged BOD, COD, TN and TP were generally increasing as going downstream and the worst water quality were found at Goryeong and Hyunpung station. Overall, water quality of Nakdong river especially in COD, SS, and TN getting worse in time at most stations and as going downstream.

• 대한토목학회논문집
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• 제26권6B호
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• pp.583-596
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• 2006

증발은 자연생태계의 에너지 및 물수지에서 중요한 역할을 담당하고 있고, 증발량의 변화에 관한 연구는 수자원의 계획 및 운영에 있어 중요한 요소이다. 본 연구에서는 1973-2004년, 32년간의 4월-10월 사이 7개월 동안의 증발량 평균값과 각 월별 증발량의 변화경향을 파악하고 추세 분석을 위해서 Mann-Kendall 검정을 실시하였다. 또한 증발과 관련된 기상요소들 즉 기온, 강수량, 습도, 전운량, 풍정합 등과의 상관관계도 분석하였다. 전 세계 여러 지역에서 관측된 바와 동일하게 기온 및 강수량이 증가함에도 불구하고 여수와 진주를 제외하고는 모든 관측지점에서 증발량은 감소경향을 나타내었다. 연구 결과는 팬 증발량의 감소가 실제 증발량의 증가를 나타낸다는 Brutsaert와 Parlange(1998)의 해석처럼 우리나라의 팬 증발량의 감소 경향은 실제 증발량의 증가를 나타낸다고 판단된다.

• 대한수학회지
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• 제40권1호
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• pp.29-40
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• 2003

Let K be a nonempty closed bounded convex subset of an arbitrary smooth Banach space X and T : KlongrightarrowK be a strictly hemi-contractive operator. Under some conditions we obtain that the Mann iteration method with errors both converges strongly to a unique fixed point of T and is almost T-stable on K. The results presented in this paper generalize the corresponding results in [l]-[7], [20] and others.

• 대한수학회지
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• 제31권3호
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• pp.333-337
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• 1994

Many authors[3][4][5] constructed and examined some processes for the fixed point of strictly pseudocontractive mapping in various Banach spaces. In fact the fixed point of strictly pseudocontractive mapping is the zero of strongly accretive operators. So the same processes are used for the both circumstances. Reich[3] proved that Mann-iteration precess can be applied to approximate the zero of strongly accretive operator in uniformly smooth Banach spaces. In the above paper he asked whether the fact can be extended to other Banach spaces the duals of which are not necessarily uniformly convex. Recently Schu[4] proved it for uniformly continuous strictly pseudocontractive mappings in smooth Banach spaces. In this paper we proved that Mann-iteration process can be applied to approximate the fixed point of strictly pseudocontractive mapping in certain Banach spaces.

• 한국건축시공학회:학술대회논문집
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• 한국건축시공학회 2015년도 춘계 학술논문 발표대회
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• pp.221-222
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• 2015

Since the input data such as types and quantities of materials cannot be acquired during the planning and designing phases, it is difficult to estimate the carbon emissions from the construction phase. As the materials are closely related to the building usages, an approximate estimation by the usages can be suggested. However, before confirming the estimation, the difference test among the carbon emissions of the building usages should be implemented. This study executed t-test or Mann-Whitney test between apartments and schools. The result of the study statistically verified the significant difference between the carbon emissions of apartments and schools.

• Communications for Statistical Applications and Methods
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• 제5권1호
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• pp.133-144
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• 1998

In this paper, we propose the two-sample test statistic using Wilcoxon signed rank test on ranked-set sampling(RSS) and obtain the asymptotic relative efficiencies(ARE) of the proposed test statistic with respect to Mann-Whitney-Wilcoxon statistic on simple random sampling(SRS), the Mann-Whitney-Wilcoxon statistic on RSS, sign statistic on RSS and Wilcoxon signed rank test on SRS. From the simulation works, we compare the powers of the proposed test statistic, Mann-Whitney-Wilcoxon statistic on RSS, the usual two-sample t statistic, sign statistic on RSS, where the underlying distributions are uniform, normal, double exponential, logistic and Cauchy distributions.

• Communications for Statistical Applications and Methods
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• 제22권4호
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• pp.377-387
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• 2015

The area under the ROC curve can be represented by both Mann-Whitney and Wilcoxon rank sum statistics. Consider an ROC surface and manifold equal to three dimensions or more. This paper finds that the volume under the ROC surface (VUS) and the hypervolume under the ROC manifold (HUM) could be derived as functions of both conditional Mann-Whitney statistics and conditional Wilcoxon rank sum statistics. The nullhypothesis equal to three distribution functions or more are identical can be tested using VUS and HUM statistics based on the asymptotic large sample theory of Wilcoxon rank sum statistics. Illustrative examples with three and four random samples show that two approaches give the same VUS and $HUM^4$. The equivalence of several distribution functions is also tested with VUS and $HUM^4$ in terms of conditional Wilcoxon rank sum statistics.

• Journal of applied mathematics & informatics
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• 제30권3_4호
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• pp.613-622
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• 2012

In this paper, we propose a new algorithm to modify the standard Mann' process to have strong convergence for $k$-strictly pseudo-contractive non-self mapping in Hilbert spaces.