• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.543-559
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• 2002

Some inequalities and approximations for the finite filbert transform by the use of Ostrowski type inequalities for absolutely continuous functions are given.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.213-230
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• 2005

Companions of Ostrowski's integral inequality for absolutely continuous functions and applications for composite quadrature rules and for p.d.J.'s are provided.

• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.15-35
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• 2010

By strengthening dichotomy condition and weakening decay conditions, we show that a four term 2n-th order differential operator with unbounded coefficients is nonlimit-point. Using stringent conditions we show that the deficiency index of this operator is determined by the behaviour of the coefficients themselves. Similarly, we prove the absence of singular continuous spectrum and that the absolutely continuous spectrum has multiplicity two.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.763-780
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• 2008

An Ostrowski type inequality is developed for estimating the deviation of the integral mean of an absolutely continuous function, and the linear combination of its values at k + 1 partition points, on a segment of (real) linear spaces. Several particular cases are provided which recapture some earlier results, along with the results for trapezoidal type inequalities and the classical Ostrowski inequality. Some inequalities are obtained by applying these results for semi-inner products; and some of these inequalities are proven to be sharp.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.243-247
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• 2014

Let {$X_n$, $n{\geq}1$} be a sequence of i.i.d. random variables with absolutely continuous cumulative distribution function(cdf) F(x) and the corresponding probability density function(pdf) f(x). In this paper, we give characterizations of Pareto and Weibull distribution by considering conditional expectations of record values.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.1
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• pp.17-31
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• 2002

Using some techniques developed by Dragomir and Wang in the recent paper [2] in connection to Ostrowski integral inequality, we point out some approximation results for the Henkel's transform of absolutely continuous mapping.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.149-153
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• 2009

Let {$X_{n},\;n\;\geq\;1$} be a sequence of independent and identically distributed random variables with absolutely continuous cumulative distribution function (cdf) F(x) and probability density function (pdf) f(x). Suppose $X_{U(m)},\;m = 1,\;2,\;{\cdots}$ be the upper record values of {$X_{n},\;n\;\geq\;1$}. It is shown that the linearity of the conditional expectation of $X_{U(n+2)}$ given $X_{U(n)}$ characterizes the lomax, exponential and pareto distributions.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.501-505
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• 2012

In this paper, general classes of continuous distributions are characterized by considering the conditional expectations of functions of upper record statistics. The specific distribution considered as a particular case of the general class of distribution are Exponential, Exponential Power(EP), Inverse Weibull, Beta Gumbel, Modified Weibull(MW), Weibull, Pareto, Power, Singh-Maddala, Gumbel, Rayleigh, Gompertz, Extream value 1, Beta of the first kind, Beta of the second kind and Lomax.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.651-657
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• 2017

A sequence {$X_n,\;n{\geq}1$} of independent and identically distributed random variables with absolutely continuous (with respect to Lebesque measure) cumulative distribution function F(x) is considered. We obtain two characterizations of a family of continuous probability distribution by independence property of record values.

• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.899-924
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• 2010

In the paper we introduce averages of each type and use these averages to construct examples of weakly compact operators on the space C ($\Omega$) for which the necessary and sufficient conditions that they be compact, absolutely summing or nuclear are distinct. A great number of concrete examples, in various situations, are given.