• Communications for Statistical Applications and Methods
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• v.12 no.2
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• pp.473-481
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• 2005

The testing problem for sphericity structure of the covariance matrix in a multivariate normal distribution is introduced when there is a sample with 2-step monotone missing data pattern. The maximum likelihood method is described to estimate the parameters on the basis of the sample. Using these estimates, the likelihood ratio criterion for testing sphericity is derived.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.63-74
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• 2012

Based on the Hilbert $C^*$-module structure we study the reconstruction theorem for stationary monotone quantum Markov processes from quantum dynamical semigroups. We prove that the quantum stochastic monotone process constructed from a covariant quantum dynamical semigroup is again covariant in the strong sense.

• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.233-240
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• 2019

In the present paper, absolute matrix summability of infinite series is studied. A new theorem concerning absolute matrix summability factors, which generalizes a known theorem dealing with absolute Riesz summability factors of infinite series, is proved using almost increasing and ${\delta}$-quasi-monotone sequences. Also, a result dealing with absolute $Ces{\grave{a}}ro$ summability is given.

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.101-123
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• 2019

In this paper, we consider a system of nonlinear variational type inclusions involving ($H,{\varphi},{\eta}$)-monotone operators in real Banach spaces. Further, we define a proximal operator associated with an ($H,{\varphi},{\eta}$)-monotone operator and show that it is single valued and Lipschitz continuous. Using proximal point operator techniques, we prove the existence and uniqueness of a solution and suggest an iterative algorithm for the system of nonlinear variational type inclusions. Furthermore, we discuss the convergence of the iterative sequences generated by the algorithms.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.613-629
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• 2021

In this paper, we present and prove new existence and uniqueness fixed point theorems for vector operators having a mixed monotone property in partially ordered product Banach spaces. Our results extend and improve existing works on τ-φ-concave operators in the scalar case. As an application, we study the existence and uniqueness of positive solutions for systems of nonlinear Neumann boundary value problems.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.681-699
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• 2020

In this paper, topological entropy of iterated function systems (IFS) on one dimensional spaces is considered. Estimation of an upper bound of topological entropy of piecewise monotone IFS is obtained by open covers. Then, we provide a way to calculate topological entropy of piecewise monotone IFS. In the following, some examples are given to illustrate our theoretical results. Finally, we have a discussion about the possible applications of these examples in various sciences.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.53-67
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• 2022

Nonlinear system of initial value problems involving R-L fractional derivative is studied. Monotone iterative technique coupled with lower and upper solutions is developed for the problem. It is successfully applied to study qualitative properties of solutions of nonlinear system of initial value problem when the function on the right hand side is nondecreasing.

• East Asian mathematical journal
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• v.27 no.1
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• pp.1-9
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• 2011

In this paper, we consider an iterative scheme for finding a common element of the set of fixed points of a asymptotically quasi nonexpansive mapping and the set of solutions of the variational inequality for an inverse strongly monotone mapping in a Hilbert space. Then we show that the sequence converges strongly to a common element of two sets. Using this result, we consider the problem of finding a common fixed point of a asymptotically quasi-nonexpansive mapping and strictly pseudocontractive mapping and the problem of finding a common element of the set of fixed points of a asymptotically quasi-nonexpansive mapping and the set of zeros of an inverse-strongly monotone mapping.

• Communications for Statistical Applications and Methods
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• v.15 no.5
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• pp.675-685
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• 2008

This paper studies two sequential procedures to estimate a monotone convex function using $L_2$ monotonization and uniform convexification; one, denoted by FMSC, monotonizes the data first and then, convexifis the monotone estimate; the other, denoted by FCSM, first convexifies the data and then monotonizes the convex estimate. We show that two shape modifiers are not commutable and so does FMSC and FCSM. We compare them numerically in uniform error(UE) and integrated mean squared error(IMSE). The results show that FMSC has smaller uniform error(UE) and integrated mean squared error(IMSE) than those of FCSC.

• Proceedings of the Korean Statistical Society Conference
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• 2004.11a
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• pp.1-8
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• 2004

We address the problem of parameter estimation in multivariate distributions under ignorable non-monotone missing data. The factoring likelihood method for monotone missing data, termed by Robin (1974), is extended to a more general case of non-monotone missing data. The proposed method is algebraically equivalent to the Newton-Raphson method for the observed likelihood, but avoids the burden of computing the first and the second partial derivatives of the observed likelihood Instead, the maximum likelihood estimates and their information matrices for each partition of the data set are computed separately and combined naturally using the generalized least squares method. A numerical example is also presented to illustrate the method.