• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.71-82
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• 2012

In this paper, we first show the weak convergence of the modified Ishikawa iteration process with errors of two total asymptotically nonexpansive mappings, which generalizes the result due to Khan and Fukhar-ud-din [1]. Next, we show the strong convergence of the modified Ishikawa iteration process with errors of two total asymptotically nonexpansive mappings satisfying Condition ($\mathbf{A}^{\prime}$), which generalizes the result due to Fukhar-ud-din and Khan [2].

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1269-1279
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• 2014

The equations arising from the thermoelastic theory are analyzed in a linear approximation. First, we establish the convergence result on the coefficient c. Next, we establish that the solution depends continuously on changes in the coefficient c. The main tool used in this paper is the energy method.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.137-162
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• 2014

In this work we study the local and semilocal convergence of the relaxed Newton's method, that is Newton's method with a relaxation parameter 0 < ${\lambda}$ < 2. We give a Kantorovich-like theorem that can be applied for operators defined between two Banach spaces. In fact, we obtain the recurrent sequence that majorizes the one given by the method and we characterize its convergence by a result that involves the relaxation parameter ${\lambda}$. We use a new technique that allows us on the one hand to generalize and on the other hand to extend the applicability of the result given initially by Kantorovich for ${\lambda}=1$.

• The Pure and Applied Mathematics
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• v.25 no.2
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• pp.149-160
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• 2018

In this paper, we prove a strong convergence result under an iterative scheme for N finite asymptotically $k_i-strictly$ pseudo-contractive mappings and a firmly nonexpansive mappings $S_r$. Then, we modify this algorithm to obtain a strong convergence result by hybrid methods. Our results extend and unify the corresponding ones in [1, 2, 3, 8]. In particular, some necessary and sufficient conditions for strong convergence under Algorithm 1.1 are obtained.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1351-1361
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• 2011

We in this paper study the complete convergence and almost surely convergence for arrays of rowwise pairwise negatively dependent(ND) random variables (r.${\upsilon}$.'s) which are dominated randomly by some random variables and obtain a result dealing with complete convergence of linear processes.

• Journal of the Korean Statistical Society
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• v.26 no.2
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• pp.231-243
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• 1997

In this paper we investigate weak convergence of the intergral processes whose index set is the non-compact infinite time interval. Our first goal is to develop the empirical central limit theorem as random elements of [0, .infty.) for an integral process which is constructed from iid variables. In developing the weak convergence as random elements of D[0, .infty.), we will use a result of Ossiander(4) whose proof heavily depends on the total boundedness of the index set. Our next goal is to establish the empirical central limit theorem for the Kaplan-Meier integral process as random elements of D[0, .infty.). In achieving the the goal, we will use the above iid result, a representation of State(6) on the Kaplan-Meier integral, and a lemma on the uniform order of convergence. The first result, in some sense, generalizes the result of empirical central limit therem of Pollard(5) where the process is regarded as random elements of D[-.infty., .infty.] and the sample paths of limiting Gaussian process may jump. The second result generalizes the first result to random censorship model. The later also generalizes one dimensional central limit theorem of Stute(6) to a process version. These results may be used in the nonparametric statistical inference.

• Journal of the Korean earth science society
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• v.41 no.6
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• pp.670-683
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• 2020

The purpose of this study was to develop a test tool for convergence problem solving skill. To this end, constructs of convergence problem solving skill were defined in three domains: convergence attributes, convergence thinking, and convergence literacy domains. Thirty-seven pilot items were developed on the basis of the sub-categories for each domain that was defined through intensive literature review; problem solving & convergent thinking and creative thinking for convergence thinking domain, individual and social propensity for the convergence attributes domain, and convergence literacy as convergence literacy domain. Through an exploratory factor analysis, 30 items in the constructs of the test tool were confirmed. A confirmatory factor analysis result showed that the five construct models well captured the covariance between all the items well. Finally a statistical result shows that the reliability of the items and constructs were well established (Cronbach's α value= .963). Thus, the test tool for convergence problem solving skill developed in this study was statistically reliable.

• The Journal of the Korea Contents Association
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• v.18 no.6
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• pp.667-678
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• 2018

The purpose of this study is to investigate empirically the factors affecting the research results of humanities and social sciences based convergence research. For this purpose, personal characteristics, research environment factor, researcher factor, research team factor, and support agency factor were set as influence factors of convergence research. Survey was conducted for researchers who are conducting research on humanities and social sciences based convergence research. As a result, it was found that factors influencing research on humanities and social sciences based convergence were researcher factor, supporting agency factor, research environment factor(major), and the influence of these factors on convergence research result was 51.6%. The implications of the research results are as follows: First, when performing the convergence research based on humanities and social science, individual factor of the researcher is more important than the factor of the research team in the performance of convergence research. Second, the support organization can improve the convergence research result through continuous management of convergence research results. Third, the research field (major) of the researcher also influences the performance of the convergence research. Therefore, the research field (major) should be considered important in the formation of the convergence research team.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.507-519
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• 2012

In this paper we obtain the complete moment convergence for an array of rowwise extended negative orthant dependent random variables. By using the result we can prove the complete moment convergence for some positively orthant dependent sequence satisfying the extended negative orthant dependence.

• East Asian mathematical journal
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• v.23 no.2
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• pp.261-270
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• 2007

We provide a local convergence analysis for Secant-like algorithm for solving nonsmooth variational inclusions in Banach spaces. An existence-convergence theorem and an improvement of the ratio of convergence of this algorithm are given under center-conditioned divided difference and Aubin's continuity concept. Our result compare favorably with related obtained in [16].